ࡱ> mq ebjbjt+t+ %AAI^Q]PPPPd+d+d+x+x+x+x+8+,x+T .v1"111???$ x?d+?H???? PP11+ .   ? Pb1(d+1x+x+PPPP? >  d+1-D`\x+x+Chapter 6. Uniform Acceleration Problems: Speed and Velocity 6-1. A car travels a distance of 86 km at an average speed of 8 m/s. How many hours were required for the trip?  EMBED Equation   EMBED Equation.DSMT4  t = 2.99 h 6-2. Sound travels at an average speed of 340 m/s. Lightning from a distant thundercloud is seen almost immediately. If the sound of thunder reaches the ear 3 s later, how far away is the storm?  EMBED Equation  t = 58.8 ms 6-3. A small rocket leaves its pad and travels a distance of 40 m vertically upward before returning to the earth five seconds after it was launched. What was the average velocity for the trip?  EMBED Equation  v = 16.0 m/s 6-4. A car travels along a U-shaped curve for a distance of 400 m in 30 s. Its final location, however is only 40 m from the starting position. What is the average speed and what is the magnitude of the average velocity?  Average speed:  EMBED Equation  v = 13.3 m/s  Average velocity:  EMBED Equation  v = 1.33 m/s, E 6-5. A woman walks for 4 min directly north with a average velocity of 6 km/h; then she walks eastward at 4 km/h for 10 min. What is her average speed for the trip? t1 = 4 min = 0.0667 h; t2 = 10 min = 0.167 h s1 = v1t1 = (6 km/h)(0.0667 h) = 0.400 km s1 = v2t2 = (4 km/h)(0.167 h) = 0.667 km   EMBED Equation  v = 4.57 km/h 6-6. What is the average velocity for the entire trip described in Problem 6-5?  EMBED Equation  D = 0.778 km, 31.00  EMBED Equation  v = 3.33 km/h, 31.00 6-7. A car travels at an average speed of 60 mi/h for 3 h and 20 min. What was the distance?  t = 3 h + 0.333 h = 3.33 h; s = vt = (60 mi/h)(3.33 h); s = 200 mi  6.8 How long will it take to travel 400 km if the average speed is 90 km/h?  EMBED Equation  t = 4.44 h *6-9. A marble rolls up an inclined ramp a distance of 5 m, then stops and returns to a point 5 m below its starting point. The entire trip took only 2 s. What was the average speed and what was the average velocity? (s1 = 5 m, s2 = -10 m)  speed =  EMBED Equation  v = 7.50 m/s velocity =  EMBED Equation  v = 2.5 m/s, down plane. Uniform Acceleration 6-10. The tip of a robot arm is moving to the right at 8 m/s. Four seconds later, it is moving to the left at 2 m/s. What is the change in velocity and what is the acceleration. (v = vf - vo = (2 m/s) (8 m/s) (v = 10 m/s  EMBED Equation  a = 2.50 m/s2 6-11. An arrow accelerates from zero to 40 m/s in the 0.5 s it is in contact with the bow string. What is the average acceleration?  EMBED Equation  a = 80.0 m/s2  6-12. A car traveling initially at 50 km/h accelerates at a rate of 4 m/s2 for 3 s. What is the final speed? vo = 50 km/h = 13.9 m/s; vf = vo + at vf = (13.9 m/s) + (4 m/s2)(3 s) = 25.9 m/s; vf = 25.9 m/s  6-13. A truck traveling at 60 mi/h brakes to a stop in 180 ft. What was the average acceleration and stopping time? vo = 60 mi/h = 88.0 ft/s 2as = vf2 vo2  EMBED Equation.DSMT4  a = 21.5 ft/s2  EMBED Equation.DSMT4  t = 4.09 s 6-14. An arresting device on a carrier deck stops an airplane in 1.5 s. The average acceleration was 49 m/s2. What was the stopping distance? What was the initial speed? vf = vo + at; 0 = vo + ( 49 m/s2)(1.5 s); vo = 73.5 m/s s = vf t - at2 ; s = (0)(1.5 s) (-49 m/s2)(1.5 s)2; s = 55.1 m 6-15. In a braking test, a car traveling at 60 km/h is stopped in a time of 3 s. What was the acceleration and stopping distance? ( vo = 60 km/h = 16.7 m/s) vf = vo + at; (0) = (16.7 m/s) + a (3 s); a = 5.56 m/s2  EMBED Equation.DSMT4 ; s = 25.0 m 6-16. A bullet leaves a 28-in. rifle barrel at 2700 ft/s. What was its acceleration and time in the barrel? (s = 28 in. = 2.33 ft) 2as = vo2 - vf2 ;  EMBED Equation ; a = 1.56 x 106 m/s2  EMBED Equation ; t = 1.73 ms 6-17. The ball in Fig. 6-13 is given an initial velocity of 16 m/s at the bottom of an inclined plane. Two seconds later it is still moving up the plane, but with a velocity of only 4 m/s. What is the acceleration? vf = vo + at;  EMBED Equation ; a = -6.00 m/s2 6-18. For Problem 6-17, what is the maximum displacement from the bottom and what is the velocity 4 s after leaving the bottom? (Maximum displacement occurs when vf = 0) 2as = vo2 - vf2;  EMBED Equation ; s = +21.3 m vf = vo + at = 16 m/s = (-6 m/s2)(4 s); vf = - 8.00 m/s, down plane 6-19. A monorail train traveling at 80 km/h must be stopped in a distance of 40 m. What average acceleration is required and what is the stopping time? ( vo = 80 km/h = 22.2 m/s) 2as = vo2 - vf2;  EMBED Equation ; a = -6.17 m/s2  EMBED Equation  ; t = 3.60 m/s Gravity and Free-Falling Bodies 6-20. A ball is dropped from rest and falls for 5 s. What are its position and velocity? s = vot + at2; s = (0)(5 s) + (-9.8 m/s2)(5 s)2 ; s = -122.5 m vf = vo + at = 0 + (-9.8 m/s2)(5 s); v = -49.0 m/s  6-21. A rock is dropped from rest. When will its displacement be 18 m below the point of release? What is its velocity at that time? s = vot + at2; (-18 m) = (0)(t) + (-9.8 m/s2)t2 ; t = 1.92 s vf = vo + at = 0 + (-9.8 m/s2)(1.92 s); vf = -18.8 m/s  6-22. A woman drops a weight from the top of a bridge while a friend below measures the time to strike the water below. What is the height of the bridge if the time is 3 s? s = vot + at2 = (0) + (-9.8 m/s2)(3 s)2; s = -44.1 m  6-23. A brick is given an initial downward velocity of 6 m/s. What is its final velocity after falling a distance of 40 m? 2as = vo2 - vf2 ;  EMBED Equation ; v = (28.6 m/s; Since velocity is downward, v = - 28.6 m/s 6-24. A projectile is thrown vertically upward and returns to its starting position in 5 s. What was its initial velocity and how high did it rise? s = vot + at2; 0 = vo(5 s) + (-9.8 m/s2)(5 s)2 ; vo = 24.5 m/s It rises until vf = 0; 2as = vo2 - vf2 ;  EMBED Equation ; s = 30.6 m 6-25. An arrow is shot vertically upward with an initial velocity of 80 ft/s. What is its maximum height? (At maximum height, vf = 0; a = g = -32 ft/s2) 2as = vo2 - vf2;  EMBED Equation ; s = 100 ft 6-26. In Problem 6-25, what are the position and velocity of the arrow after 2 s and after 6 s? s = vot + at2 = (80 ft/s)(2 s) + (-32 ft/s2)(2 s)2 ; s = 96 ft vf = vo + at = (80 ft/s) + (-32 ft/s2)(2 s); vf = 16 ft/s s = vot + at2 = (80 ft/s)(6 s) + (-32 ft/s2)(6 s)2 ; s = -96 ft vf = vo + at = (80 ft/s) + (-32 ft/s2)(6 s); vf = -112 ft/s  6-27. A hammer is thrown vertically upward to the top of a roof 16 m high. What minimum initial velocity was required? 2as = vo2 - vf2 ;  EMBED Equation ; vo = 17.7 m/s Horizontal Projection 6-28. A baseball leaves a bat with a horizontal velocity of 20 m/s. In a time of 0.25 s, how far will it have traveled horizontally and how far has it fallen vertically? x = vox t = (20 m/s)(2.5 s) ; x = 50.0 m y = voy + gt2 = (0)(2.5 s) + (-9.8 m/s2)(0.25 s)2 y = -0.306 m 6-29. An airplane traveling at 70 m/s drops a box of supplies. What horizontal distance will the box travel before striking the ground 340 m below? First we find the time to fall: y = voy t + gt2  EMBED Equation  t = 8.33 s ; x = vox t = (70 m/s)(8.33 s) ; x = 583 m  6-30. At a lumber mill, logs are discharged horizontally at 15 m/s from a greased chute that is 20 m above a mill pond. How far do the logs travel horizontally? y = gt2;  EMBED Equation ; t = 2.02 s x = vox t = (15 m/s)(8.33 s) ; x = 30.3 m  6-31. A steel ball rolls off the edge of a table top 4 ft above the floor. If it strikes the floor 5 ft from the base of the table, what was its initial horizontal speed? First find time to drop 4 ft:  EMBED Equation ; t = 0.500 s x = vox t ;  EMBED Equation  ; vox = 10.0 ft/s 6-32. A bullet leaves the barrel of a weapon with an initial horizontal velocity of 400 m/s. Find the horizontal and vertical displacements after 3 s. x = vox t = (400 m/s)(3 s) ; x = 1200 m y = voy + gt2 = (0)(3 s) + (-9.8 m/s2)(3 s)2 y = -44.1 m  6-33. A projectile has an initial horizontal velocity of 40 m/s at the edge of a roof top. Find the horizontal and vertical components of its velocity after 3 s. vx = vox = 40 m/s vy = voy t + gt = 0 + (-9.8 m/s2)(3s); vy = -29.4 m/s The More General Problem of Trajectories 6-34. A stone is given an initial velocity of 20 m/s at an angle of 580. What are its horizontal and vertical displacements after 3 s? vox = (20 m/s) cos 580 = 10.6 m/s; voy = (20 m/s) sin 580 = 17.0 m/s x = voxt = (10.6 m/s)(3 s); x = 31.8 m y = voyt + gt2 = (17.0 m/s)(3 s) +(-9.8 m/s2)(3 s)2; y = 6.78 m  6-35. A baseball leaves the bat with a velocity of 30 m/s at an angle of 300. What are the horizontal and vertical components of its velocity after 3 s? vox = (30 m/s) cos 300 = 26.0 m/s; voy = (30 m/s) sin 300 = 15.0 m/s vx = vox = 26.0 m/s ; vx = 26.0 m/s vy = voy + gt = (15 m/s) + (-9.8 m/s2)(3 s) ; vy = -14.4 m/s  6-36. For the baseball in Problem 6-33, what is the maximum height and what is the range? ymax occurs when vy = 0, or when: vy = voy + gt = 0 and t = - voy/g   EMBED Equation ; Now we find ymax using this time. ymax = voyt + gt2 = (15 m/s)(1.53 s) + (-9.8 m/s2)(1.53 s)2; ymax = 11.5 m  The range will be reached when the time is t = 2(1.53 s) or t = 3.06 s, thus R = voxt= (30 m/s) cos 300 (3.06 s); R = 79.5 m  6-37. An arrow leaves the bow with an initial velocity of 120 ft/s at an angle of 370 with the horizontal. What are the horizontal and vertical components of is displacement two seconds later? vox = (120 ft/s) cos 370 = 104 ft/s; voy = (120 ft/s) sin 300 = 60.0 ft/s 6-37. (Cont.) The components of the initial velocity are: vox = 104 ft/s; voy = 60.0 ft/s x = voxt = (104 ft/s)(2 s); x = 208 ft y = voyt + gt2 = (60.0 m/s)(2 s) +(-32 ft/s2)(2 s)2; y = 56.0 ft  *6-38. In Problem 6-37, what are the magnitude and direction of arrows velocity after 2 s? vx = vox = 104 ft/s ; vx = 104 ft/s vy = voy + gt = (60 m/s) + (-32 ft/s2)(2 s) ; vy = -4.00 ft/s  *6-39. A golf ball in Fig. 6-14 leaves the tee with a velocity of 40 m/s at 650. If it lands on a green located 10 m higher than the tee, what was the time of flight, and what was the horizontal distance to the tee? vox = (40 m/s) cos 650 = 16.9 m/s; voy = (40 m/s) sin 650 = 36.25 m/s y = voyt + gt2: 10 ft = (36.25 m/s) t + (-9.8 m/s2)t2 Solving quadratic (4.9t2 36.25t + 10 = 0) yields: t1 = 0.287 s and t2 = 7.11 s The first time is for y = +10 m on the way up, the second is y = +10 m on the way down. Thus, the time from tee to green was: t = 7.11 s Horizontal distance to tee: x = voxt = (16.9 m/s)(7.11 s); x = 120 m  *6-40. A projectile leaves the ground with a velocity of 35 m/s at an angle of 320. What is the maximum height attained. vox = (35 m/s) cos 320 = 29.7 m/s; voy = (35 m/s) sin 320 = 18.55 m/s ymax occurs when vy = 0, or when: vy = voy + gt = 0 and t = - voy/g   EMBED Equation ; Now we find ymax using this time. ymax = voyt + gt2 = (18.55 m/s)(1.89 s) + (-9.8 m/s2)(1.89 s)2; ymax = 17.5 m *6-41. The projectile in Problem 6-40 rises and falls, striking a billboard at a point 8 m above the ground. What was the time of flight and how far did it travel horizontally. vox = (35 m/s) cos 320 = 29.7 m/s; voy = (35 m/s) sin 320 = 18.55 m/s y = voyt + gt2: 8 m = (18.55 m/s) t + (-9.8 m/s2)t2 Solving quadratic (4.9t2 18.55t + 8 = 0) yields: t1 = 0.497 s and t2 = 3.36 s The first time is for y = +8 m on the way up, the second is y = +8 m on the way down. Thus, the time from tee to green was: t = 3.29 s Horizontal distance to tee: x = voxt = (29.7 m/s)(3.29 s); x = 97.7 m Challenge Problems 6-42. A rocket travels in space at 60 m/s before it is given a sudden acceleration. Its velocity increases to 140 m/s in 8 s, what was its average acceleration and how far did it travel in this time?  EMBED Equation ; a = 10 m/s2  EMBED Equation ; t = 800 s  6-43. A railroad car starts from rest and coasts freely down an incline. With an average acceleration of 4 ft/s2, what will be the velocity after 5 s? What distance does it travel? vf = vo + at = 0 + (4 ft/s2)(5 s); vf = 20 ft/s s = vot + at2 = 0 + (4 ft/s2)(5 s)2; s = 50 ft *6-44. An object is projected horizontally at 20 m/s. At the same time, another object located 12 m down range is dropped from rest. When will they collide and how far are they located below the release point? A: vox = 20 m/s, voy = 0; B: vox = voy = 0 Ball B will have fallen the distance y at the same time t as ball A. Thus, x = voxt and (20 m/s)t = 12 m; t = 0.600 s y = at2 = (-9.8 m/s2)(0.6 s)2 ; y = -1.76 m  6-45. A truck moving at an initial velocity of 30 m/s is brought to a stop in 10 s. What was the acceleration of the car and what was the stopping distance?  EMBED Equation ; a = -3.00 m/s2  EMBED Equation ; s = 150 m 6-46. A ball is thrown vertically upward with an initial velocity of 23 m/s. What are its position and velocity after 2s, after 4 s, and after 8 s?  Apply s = vot + at2 and vf = vo + at for time of 2, 4, and 8 s:  (a) s = (23 m/s)(2 s) + (-9.8 m/s2)(2 s)2 ; s = 26.4 m  vf = (23 m/s) + (-9.8 m/s2)(2 s) ; vf = 3.40 m/s  (b) s = (23 m/s)(4 s) + (-9.8 m/s2)(4 s)2 ; s = 13.6 m  vf = (23 m/s) + (-9.8 m/s2)(4 s) ; vf = -16.2 m/s  (c) s = (23 m/s)(8 s) + (-9.8 m/s2)(8 s)2 ; s = -130 m vf = (23 m/s) + (-9.8 m/s2)(8 s) ; vf = -55.4 m/s 6-47. A stone is thrown vertically downward from the top of a bridge. Four seconds later it strikes the water below. If the final velocity was 60 m/s. What was the initial velocity of the stone and how high was the bridge? vf = vo + at; v0 = vf at = (-60 m/s) - (-9.8 m/s)(4 s); vo = -20.8 m/s s = vot + at2 = (-20.8 m/s)(4 s) + (-9.8 m/s)(4 s)2; s = 162 m  6-48. A ball is thrown vertically upward with an initial velocity of 80 ft/s. What are its position and velocity after (a) 1 s; (b) 3 s; and (c) 6 s Apply s = vot + at2 and vf = vo + at for time of 2, 4, and 8 s:  (a) s = (80 ft/s)(1 s) + (-32 ft/s2)(1 s)2 ; s = 64.0 ft  vf = (80 ft/s) + (-32 ft/s2)(2 s) ; vf = 16.0 ft/s (b) s = (80 ft/s)(3 s) + (-32 ft/s2)(3 s)2 ; s = 96.0 ft  vf = (80 ft/s) + (-32 ft/s2)(3 s) ; vf = -16.0 ft/s (c) s = (80 ft/s)(6 s) + (-32 ft/s2)(6 s)2 ; s = 64.0 ft vf = (80 ft/s) + (-32 ft/s2)(6 s) ; vf = -96.0 ft/s  6-49. An aircraft flying horizontally at 500 mi/h releases a package. Four seconds later, the package strikes the ground below. What was the altitude of the plane? y = gt2 = (-32 ft/s2)(4 s)2; y = -256 ft *6-50. In Problem 6-49, what was the horizontal range of the package and what are the components of its final velocity? vo = 500 mi/h = 733 ft/s; vx = vox = 733 ft/s; voy = 0; t = 4 s x = vxt = (733 ft/s)(4 s); x = 2930 ft vy = voy + at = 0 + (-32 ft/s)(4 s); vy = -128 ft/s; vx = 733 m/s *6-51. A putting green is located 240 ft horizontally and 64 ft vertically from the tee. What must be the magnitude and direction of the initial velocity if a ball is to strike the green at this location after a time of 4 s? x = voxt; 240 ft = vox (4 s); vox = 60 m/s s = vot + at2; 64 ft = voy(4 s) + (-32 ft/s2)(4 s)2; voy = 80 ft/s  EMBED Equation ;  EMBED Equation  v = 100 ft/s, ( = 53.10 Critical Thinking Questions 6-52. A long strip of pavement is marked off in 100-m intervals. Students use stopwatches to record the times a car passes each mark. The following data is listed: Distance, m010 m20 m30 m40 m50 mTime, s02.1 s4.3 s6.4 s8.4 s10.5 s Plot a graph with distance along the y-axis and time along the x-axis. What is the significance of the slope of this curve? What is the average speed of the car? At what instant in time is the distance equal to 34 m? What is the acceleration of the car? Data taken directly from the graph (not drawn): Ans. Slope is v, 4.76 m/s, 7.14 s, 0. 6-53. An astronaut tests gravity on the moon by dropping a tool from a height of 5 m. The following data are recorded electronically. Height, m5.00 m4.00 m3.00 m2.00 m1.00 m0 mTime, s01.11 s1.56 s1.92 s2.21 s2.47 s 6-53. (Cont.) Plot the graph of this data. Is it a straight line? What is the average speed for the entire fall? What is the acceleration? How would you compare this with gravity on earth? Data taken directly from the graph (not drawn): Ans. Slope is v, 4.76 m/s, 7.14 s, 0. *6-54. A car is traveling initially North at 20 m/s. After traveling a distance of 6 m, the car passes point A where it's velocity is still northward but is reduced to 5 m/s. (a) What are the magnitude and direction of the acceleration of the car? (b) What time was required? (c) If the acceleration is held constant, what will be the velocity of the car when it returns to point A?  (a) vo = 20 m/s, vf = 5 m/s, x = 6 m 2as = vo2 - vf2; EMBED Equation.DSMT4 ; a = -31.2 m/s2  (b)  EMBED Equation.DSMT4 ; t = 0.480 s (c) Starts at A with vo = + 5 m/s then returns to A with zero net displacement (s = 0):  2as = vo2 - vf2; 0 = (5 m/s)2 vf2;  EMBED Equation ; vf = - 5 m/s  *6-55. A ball moving up an incline is initially located 6 m from the bottom of an incline and has a velocity of 4 m/s. Five seconds later, it is located 3 m from the bottom. Assuming constant acceleration, what was the average velocity? What is the meaning of a negative average velocity? What is the average acceleration and final velocity? vo = + 4 m/s; s = -3 m; t = 5 s Find vavg s = vavg t;  EMBED Equation  vavg = -0.600 m/s Negative average velocity means that the velocity was down the plane most of the time.  *6-55. (Cont.) s = vot + at2; -3 m = (4 m/s)(5 s) + a (5 s)2; a = -1.84 m/s2 vf = vo + at = 4 m/s + (-1.84 m/s2)(5 s); vf = -5.20 m/s  *6-56. The acceleration due to gravity on an distant planet is determined to be one-fourth its value on the earth. Does this mean that a ball dropped from a height of 4 m above this planet will strike the ground in one-fourth the time? What are the times required on the planet and on earth? The distance as a function of time is given by: s = at2 so that one-fourth the acceleration should result in twice the drop time.  EMBED Equation  te = 0.904 s  EMBED Equation  tp = 1.81 s  *6-57. Consider the two balls A and B shown in Fig. 6-15. Ball A has a constant acceleration of 4 m/s2 directed to the right, and ball B has a constant acceleration of 2 m/s2 directed to the left. Ball A is initially traveling to the left at 2 m/s, while ball B is traveling to the left initially at 5 m/s. Find the time t at which the balls collide. Also, assuming x = 0 at the initial position of ball A, what is their common displacement when they collide? Equations of displacement for A and B: s = so + vot + at2 (watch signs) For A: sA = 0 + (-2 m/s)t + (+4 m/s2) t2 For B: sB = 18 m + (-5 m/s)t + (-2 m/s2) t2; Next simplify and set sA = sB - 2t + 2t2 = 18 5t - t2 ( 3t2 + 3t 18 = 0 ( t1 = - 3 s, t2 = +2 s  Accept t = +3 s as meaningful answer, then substitute to find either sA or sB: sA = -2(2 s) + 2(2 s)2; x = + 4 m *6-58. Initially, a truck with a velocity of 40 ft/s is located distance of 500 ft to the right of a car. If the car begins at rest and accelerates at 10 ft/s2, when will it overtake the truck? How far is the point from the initial position of the car? Equations of displacement for car and truck: s = so + vot + at2 (watch signs) For car: sC = 0 + (+10 ft/s2) t2 ; Truck: sT = 500 ft + (40 ft/s)t + 0; Set sC = sT 5t2 = 500 + 40t or t2 8t 100 = 0; t1 = -6.77 s; t2 = +14.8 s Solve for either distance: sC = (10 ft/s2)(14.8 s)2; s = 1092 ft *6-59. A ball is dropped from rest at the top of a 100-m tall building. At the same instant a second ball is thrown upward from the base of the building with an initial velocity of 50 m/s. When will the two balls collide and at what distance above the street? For A: sA = 100 m + v0At + gt2 = 100 m + 0 + (-9.8 m/s2) t2  For B: sB = 0 + (50 m/s)t + (-9.8 m/s2) t2 Set sA = sB  100 4.9 t2 = 50 t 4.9 t2; 50 t = 100; t = 2.00 s Solve for s: sA = 100 m (4.9 m/s2)(2 s)2; s = 80.4 m  *6-60. A balloonist rising vertically with a velocity of 4 m/s releases a sandbag at the instant when the balloon is 16 m above the ground. Compute the position and velocity of the sandbag relative to the ground after 0.3 s and 2 s. How many seconds after its release will it strike the ground? The initial velocity of the bag is that of the balloon: voB = + 4 m/s  From ground: s = soB + voBt + gt2; s = 18 m + (4 m/s)t + (-9.8 m/s2)t2 s = 18 m + (4 m/s)(0.3 s) (4.9 m/s2)(0.3 s)2 ; s = 16.8 m *6-61. An arrow is shot upward with a velocity of 40 m/s. Three seconds later, another arrow is shot upward with a velocity of 60 m/s. At what time and position will they meet? Let t1 = t be time for first arrow, then t2 = t - 3 for second arrow. s1 = (40 m/s)t1 + (-9.8 m/s2)t12 ; s1 = 40t 4.9t2 s2 = (60 m/s)t2 + (-9.8 m/s2)t22 ; s2 = 60(t 3) - 4.9(t 3)2  s1 = s2; 40t 4.9t2 = 60t 180 4.9(t2 6t + 9)  The solution for t gives: t = 4.54 s Now find position: s1 = s2 = (40 m/s)(4.54 s) (4.9 m/s2)(4.54 s)2; s = 80.6 m  *6-62. Someone wishes to strike a target, whose horizontal range is 12 km. What must be the velocity of an object projected at an angle of 350 if it is to strike the target. What is the time of flight? y = voyt + gt2 = 0; ( vo sin 350)t = (4.9 m/s2)t2 or  EMBED Equation  R = voxt = 12 km; (vo cos 350)t = 12,000 m;  EMBED Equation  Set t = t   EMBED Equation ; From which vo = 354 m/s and t = 41.4 s *6-63. A wild boar charges directly toward a hunter with a constant speed of 60 ft/s. At the instant the boar is 100 yd away, the hunter fires an arrow at 300 with the ground. What must be the velocity of the arrow if it is to strike its target? y = 0 = (v0 sin 300)t + (-32 ft/s2)t2; Solve for t  EMBED Equation ; t = 0.03125 vo s1 =( v0 cos 300) t = (0.866 vo)(0.03125 vo); s1 = 0.0271 vo2 *6-63. (Cont.) s1 = 0.0271 vo2 ; t = 0.03125 vo vB = - 60 ft/s; soB = 300 ft s2 = soB + vBt = 300 ft + (-60 ft/s)t s2 = 300 60 (0.03125 vo) = 300 1.875 vo Now, set s1 = s2 and solve for vo  0.0271 vo2 = 300 1.875 vo or vo2 + 69.2 vo 11,070 = 0 The quadratic solution gives: vo = 76.2 ft/s Chapter 6 Uniform Acceleration Physics, 6th Edition PAGE  PAGE 64 v = -60 ft/s 300 vo s = 0 s = 300 ft s1 = s2 s1 = s2 s = 300 ft s = 0 vo 300 60 m/s 40 m/s s1 = s2 s = 100 m s = 0 B A + v = 0 v = 40 ft/s s = 500 ft s = 0 v = - 5 m/s2 v = - 2 m/s + ab = -2 m/s2 aa = +4 m/s2 x = 18 m x = 0 B s = 0 4 m/s 3 m 6 m v = 5 m/s v = 20 m/s x = 6 m A x = 0  EMBED MS_ClipArt_Gallery   EMBED MS_ClipArt_Gallery  12 m y B 0 D s2 s1 E ( D ( s2 s1 4 km/h, 10 min 6 km/h, 4 min C s = 400 m D = 40 m B A A A !",?   j EHUj: CJUVmH jEHUj: CJUVmH jEHUj<: CJUVmH6 jEHUj۬c; CJUVmH jEHUjv: CJUVmH jU jUmH5CJ5CJ 4!",?\] : h d$d d$d d d d 0d d$!",?\] : h R ; = 3 H 3c(* dJ|P{T@~ fztz"`0tv1 2 H "!h!!P"d/23DEFGLMN]^  $ % & : ? @ A C D E F G J l m n o q r s t u x ! 2 3 4 5 > ? P Q R H* jEHUj: CJUVhmHnH j-EHUj\: CJUVhmHnH6H*jUhmHnH5 j EHUj~: CJUVmH jU6j6UmH= R ; = 3 H 3c(* $0d 0dvd $vd vd $dd $dR T U f g h i t   / 1 ; < wj: CJUVhmHnHj6UhmHnH6H* jzEHUj: CJUVhmHnH jUH*hmHnH hmHnH5hmHnHj5EHUhmHnHj: CJUVhmHnH6j5UhmHnHjUhmHnH-       3 H I   &'+356GHIJTXab  &| j EHUj: CJUVhmHnHH* jEHUj : CJUVhmHnH6H* jDjUhmHnH5CJ5j6EHUj: CJUVhmHnH j6Uj6UhmHnH6 jU jEHU0&'()tu   j6UhmHnH j&EHUjɮc; CJUVhmHnH j#EHUjc; CJUVhmHnH jU6H*6H*6jUhmHnHH*B* dJ|P{T $vd vd $d$d d $0d 0d /EFNOde  ,-:>?@HIJKLMdefg  ./ƿj: CJUVhmHnH j6U j+EHUjc; CJUVhmHnH jUjUhmHnH6H*j6UhmHnHH*H*66H*B/01=IJNOPQRSdefgopTVWX\]bhiz{|}789:@BIJKOPQVWhij|: CJUVhmHnH6H* j4EHUjp: CJUVhmHnH6H* j1EHUj: CJUVhmHnH jUjUhmHnHj6UhmHnHH*6 j6Uj.6EHU3@~ fzt $vv $vd vd0vd $0d 0dijkw~cfg~  fglmtuȿjUhmHnH5CJj<6EHUjT: CJUVhmHnHj?:6EHUjM: CJUVhmHnH6H*j6UhmHnHH*6H*6 j6Ujq76EHU;z{ tu|}~ j j@EHUj: CJUVhmHnH jU6H*j6UhmHnHjUhmHnHH*66H*Jtz"`0tv1 2 H "!h!!P"" $d dv vd $vdz    !"ż jEEHUjn%: CJUVhmHnH jUj$C6EHUj : CJUVhmHnH j6Uj6UhmHnHH*6H*6H*jUhmHnH6?`afgno01267>TUefgjtu        # $ % ( 2 H I !5CJ jHEHUj;(: CJUVhmHnH jUH*6H*6H*6j6UhmHnHjUhmHnHJ!!!"!'!)!/!0!3!J!K!T!U![!\!]!`!h!i!!")","3"6":";"L"M"N"O"i"o"r"u"""""A#B#I#J#P#Q#b#c#d#e#r#y#~#######_$w$$$$ż jUjN6EHUjw.: CJUVhmHnHjK6EHUjc,: CJUVhmHnH j6Uj6UhmHnHjUhmHnHH*6H*6H*6>P"""A#y###_$$$%%%%&&' '''(b(d()I)~)))!*n** +_+++Y,,-1-y-z-|--.V.W.Y.o///G000#1%11112{22334W444455565I56<6d6f67W777d8889K9M99$:J::+;l;;;B<<<=>G>I>>+?d""A#y###_$$$%%%%&&' '''(b(d( $00 $0d 0d $vd vd $v$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&ⰧH*6H*j\T6EHUj/: CJUVhmHnH j6U6H*j6UhmHnHjUhmHnH6 jU j{QEHUj/: CJUVhmHnH?&&& 'f'g'''''''''''''''''''((("($(+(,(/(J(K(Q(R(W(X(b(c((()))))))$)()*)-)<)=)I)J)K)L)P)R)U)h)i)j)m)~))))))))))))))%*&*)*7*8*J*jUhmHnH6H*6H*j6UhmHnHH*5CJ6Ud()I)~)))!*n** +_+++Y,,-1-y-z-|--.V.v vd $0 $0d 0dJ*K*O*Q*i*k*n*o*}*~********************+ + ++d+f+j+y+z++++++++Y,Z,\,_,p,q,~,,,,,,,,,,,,,,,,,-- - --&-'-jUhmHnHH*6H*jV6EHUj?: CJUVhmHnH j6Uj6UhmHnH66H*J'-1-6-8-?-@-C-^-_-e-f-m-n-z-{-|-}------------..... .4.5.F.G.H.K.W.X...o/p/r/u////////////////////////0 0 0 0)0*0+040<0=0E0G0H0c0g0s0j6UhmHnHjUhmHnHH*6H*6H*6VV.W.Y.o///G000#1%11112{22334W4444555d0 $0d 0d $vs0t0000000000000011#1$1v1w111111111111111111 2222,2.21222@2A2R2S2T2U2f2i2~22222222222222333333ƽ6H*jY6EHUj}: CJUVhmHnH j6UH*jUhmHnH6H*j6UhmHnH66>*I333333333333333333344444448494:4D4L4M4U4W4X4s4v444444444444555 5(5,555I5666&6'6(6)60646:6;6<6=6>6O6 j\EHUj8: CJUVhmHnH jUjUhmHnH5CJ6>*j6UhmHnH6H*H*6H*6F5565I56<6d6f67W777d8889K9M99$:J::+;l;;;0 $0d $vd vdO6P6Q6R6Z6[6d6e6f6g6667 7!7"7&7'7,7:7;7J7K7L7W7\7]7d7e7t7u7{7|7777777d8l8m8o8{8|8~88888888888888888 6CJH*CJCJH*6CJ5CJ5j5CJUhmHnH6H*6H*j6UhmHnHH*jUhmHnH6 jU jR_EHUj: CJUVhmHnH=889 9999 9"9-9.96979K9L99999 : : : :::":#:$:&:':8:9:::;::::::::;;;;; ;;;+;,;6;P;Q;W;X;a;e;l;m;u;v;y;;;;;j6UhmHnH6H* jdEHUjf#: CJUVhmHnH jibEHUj": CJUVhmHnH jU5jUhmHnHH*6H*6B;;;;;;;;;;;;;<<<<<3<4<5<B<C<M<g<h<n<o<x<|<<<<<<<<<<<<=================>>>>>6>7>G>H>I>>>>>>>????? ???+?,?6?Q?R?X?6H*jUhmHnHH*6j6UhmHnH6H*W;B<<<=>G>I>>+?p??@Q@@@@AAA8B0 $0d 0dvvd $v $vd vdX?Y?d?h?p?q?y?z?}???????????????@@ @ @@$@%@A@B@C@Q@R@[@v@w@}@~@@@@@@@@@@@@@@@@AAAAAAAA8B9B:B;BBBFBGBQBWBXBYBZB^B`BcBpBqBsBBBBBBBH*6H*jUhmHnH6H*j6UhmHnH6H*V+?p??@Q@@@@AAA8BBBBDFDDDDDDEEEEEEEEEEEEEEEEEEFRGSGGGGGGHH H HHHH%H,H3H:H;HGHH H HHHH%H,H3H:Hw $0d$r$$Tl4֞ z^C!        $0$ :H;HLCLDLELFLMMMMMMMMMMMMMMMMMMMNN>NBN_NaNuNzN{NNNNN6>*jw6EHUj: CJUVmH jUmHj)u6EHUjӊ: CJUVhmHnH j6U6H*H*H*jUhmHnH66H*BKKBLCLELMMN_NNNO(PkPP Q QRS6SaSdd $0d0d0FZdvddNNNNNNNNNNNNNNNNNNNNN(P`PaPPPPPPPPPPPPPPPPPQ Q Q Q QtQuQQQR SSSSS!S?S@SCSOSTS[S\S^S_SaSbSkSlSrS~Sj|6EHUj: CJUVmHjz6EHUjͩ: CJUVmH j6Uj6UmH6H* jUmH6H*6H*F~SSSSSSSSSSSSSSSSSSSSSSSSSTTTTTNTPTTTUTWTXTYTlTmTTT&U'UUUUUUUUUUUUV V VVVV V!V(V6V7V;VAVBVGVHVLVMVUVVVkVlVVVVVVVVVVVVj6UmHH* jUmH>* j66H*6H*H*6VaSSTWTTTUUUAVVVVW4XwXXXX!Z0 & p@ P !0d & p@ P !0 $0d0ddVVVVVVWWWX X X XXXX.X/X1X2X3X4X5X6XX?X\X]X_X`XaXpXqXuXvXwXxXyXXXXXXXXXXXXXXXXXXXXXXXX"Z\Z^ZeZiZjZZZZZZZZZZZZZZ5j5UhmHnHH*jUhmHnH6H*6H*6j6UhmHnHH*PW4XwXXXX!ZiZZZ[[-\r\\\G]I]^j^^__`R``` a?auaabGbHbIbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbb b!ZiZZZ[[-\r\\\G]I]^j^^__`R``0 & p@ P !$0d & p@ P !0d & p@ P !ZZZZZZZZZZ[[[[[[[[[[\\\\\\\\\\\+\,\.\/\0\3\;\<\=\J\K\L\M\N\O\V\X\p\q\r\s\u\v\z\{\\\\\\\\\]] ] ]]*]+]4]5]G]H]]]^^!^(^)^2^3^:^;^E^H^j6UhmHnH6H*jUhmHnHH*6H*6WH^I^J^K^L^T^U^f^g^h^i^r^s^u^y^{^|^^^^^^^^^^^^^^^^^^^^^^^^^^^____&`'`(`/`0`:`?`@`A`B`C`_` jEHUj: CJUVhmHnHjUhmHnH jSEHUjl: CJUVhmHnH jU6H*j6EHUj~: CJUVhmHnH j6U6H*6H*:_```q`r`s`t`````````````````````````````aa a a!a&a(a)a3a5a?aPaQaUaWa[a\a`acadaua|a}aaaaaaaaaaaaaaaaaaaaaaaaH*j6UhmHnH6H*6H*j6EHUj-: CJUVhmHnH6 j6UO`` a?auaabGbHbIbbbbbbbbbbbbbbbb&`#$ !$0d & p@ P !aaaaaaaaaaaaabbbbb9b:b=bAbBbGbHbtbvbbbbbbbbbbbbbccccccccccccccccccccccccccccccccccccccccccccCJH* 6CJH*CJH*CJ6CJ0JmH0J j0JUH*66H*6H*Rbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbccccccccc c c c c ccccccccccccccccccc c!c"c#c$c%c&c'c(c)c*c+c,c-c.c/c0c1c2c3cdbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbccccccccc c c c c cccccccccccccccccccc c!c"c#c$c%c&c'c(c)c*c+c,c-c.c/c0c1c1c2c3c4c5c6c7c8c9c:c;cc?c@cAcBcCcDcEcFcGcHcIcJcKcLcMcNc3c4c5c6c7c8c9c:c;cc?c@cAcBcCcDcEcFcGcHcIcJcKcLcMcNcOcPcQcRcScTcUcVcWcXcYcZc[c\c]c^c_c`cacbcccdcecfcgchcicjckclcmcncocpcqcrcsctcucvcwcxcyczc{c|c}c~ccccccccccccccccccccccccccdNcOcPcQcRcScTcUcVcWcXcYcZc[c\c]c^c_c`cacbcccdcecfcgchcicjckckclcmcncocpcqcrcsctcucvcwcxcyczc{c|c}c~ccccccccccccccccccccccccccccccccccccddd d dccccccccccddd d d ddddd#d$d/d0d6d7dDdEdQdRdTdUdbdcdpdqdzd{ddddddddddddddddddddddddddd e eeeeeeeeeee e!e$e%e'e(e*e+e-e.e0e1e4e5e8e9eHeIeQeWeXeZe[eeefedcccccd ddddddd#d$d/d0d6d7d>dBdDdEdLdPdQdRdSdTdUdVdWd\d`dbdcdddedidndpdqdzd{dddddddddddddddddddddddddddddddddddddddee jUj+U: CJUVmH jU55CJ 6CJH*CJH*6CJCJS d ddddd#d$d/d0d6d7dDdEdQdRdTdUdbdcdpdqdzd{dddddddddddddddddddddddddddd e eeeeeeeeee e eeeeee e!e"e$e(e)e+e-e.e/e1e2e4e5e6e8e9eHeIeWe[e_efehevexee5CJ jq6H*65CJ jU jU#eeee e!e$e%e'e(e*e+e-e.e0e1e4e5e8e9eHeIeQeWeXeZe[eeefeoefeoepereseuevexeye{e|e}e~eeeoepereseuevexeye{e|e}e~eee0d & p@ P ! '0&PP// =!"#$%`!' O9Ȕ'DCפ<d'x{VDzug``apK !h]w[7w֦]]]j2*RNz hD3ۍt>ĈF>>?1cF4sQӧ}aYljț^E!jzҫ~^ULaW[0u]zCOxM#o {pma͇o4}|2w###ITK\lse/]Qp8888P>s< g`(hl!|W&-3qŔ9SMk\3pc3/|0?NB|;)Tdӑ%J򽒝0;v&:Z-ڞ(eܖ(f; Fd Rr<8.{6ֆ8i86lD#ݤFuܧv~S=x0C1c0S110^ng<:|$E eB (&PjFcɂzUŢ|uE W.Fk "C,j{[q.;m{WG͏6-ؘg Fw}:G*뮀2.==^Ιv''3q0٤hL|gb!)Fgbyf2XkaY' .7ԯ^j`/9`<^Nv{-L?O@ &"?&# (9crs+x{m w:GX,V %;JJ!"o"&o$d~HC$H}|Nv$G ~#ZsJtI396k!E+w_KV!DZ|NYPYDYꧠ7-:I %@>'C{Qh$JrŅ!Q~uesX^w;UnVXcn:khddDA%t,/=w=w67ly|wUo }Ut1 qu4r7ԤGMf0.&/DK\2ucq]crKM|( 6>DlM63\f `lCmm4ǧɹȵF5;:k%C G>hAr9#ؕUlW#Į%oD!f`vϜn=#(cRΣC4{{p9gO1{hg#Fb'9}mFTsXbL>d/hDv{إG] {}2'Ss0Ys5ml,֛4Xcb & (l3,1r% :1ʸ;r-u4>HGڒK$+VI"A%WJ]p>J=Dy4GKfՕddԥgz%z&dyRSVI,cd,cUߋr@Ju]2R@ݖ*ꮄ]=PdM֨Y$vz.'Co ^hz$%^&E,IS=D:Wwaэe)t٨K~]XPy'[b䐌&Rd&l2 ^ƚt2ˤe&3%Ҥ~ q}9>`- m gI[QleiiIo[S0Y@l5(nۢ攸^*Ŕ=C6xW.yNbw3̖c -No3 ^xf}hMEcf1R.٢8gk3d}v1y;ѓ~'1ŞEG=h{viUahzGFf'v+nʹ8v#f105i }#db2!51AbBGBP<֡8Ac·A: Q\gBtB|VFsOU4% XX7'8qUeWgXua8jc].ggcv;63|Z!OH'>O $K'FHԑ/E My# ,R]fJsP/Y,#@e֊jÿAu_6-[ $jIm18ğu$'t $Tº-|&jd"WS9$^ c_y6-[ΨrX%v)YIexuBcҁ\؀s˩WjS;6y%LQqZAona>T*B}|/ $C&\ W$> 4O(m$y$ J4"uer-)3l)YBFEȑj+ɱ6*N+1[;C&Nr1^s,;rݟFA,RAVK̕''#Yb<*8kKXW֒nDO/7h4`MWYvʸڗ*1}86[Όv-H쐲#EuZ cܮƌ<26c<#>/F2^LI:gG⢇x"_]yڰvl!]\sk(G\}겎 upe*ӈ QȕaYZ"]Y93p䩫%EHLf܉a}K 3\er@y|'9^zG}̽%*Pgk(MD7=1:Vr:|3 T2ABQ"i'+e›-¨$乜h$Py%͙wgf?1qCݐ guDٌh'-FB5ɸwj5 [f=Fgȭp(A1[F5AњQajbUUD8*,ǮQ^pOj(xz*RyȢ#/#VqGBGg} ֯0BX-cJN$uVeY{[ZFQèA_rSOfR=uCјwXFH]FrS׼CKƊ.\qc+6D:Jn!؏DjjH@hҘL5FlG>x/>v{\Ù1cע^6W&u }d&uyMT0YD/9|BsETn9L6`)ST%&cMf^؂ҖJ|!hb1sqJ~ ׈ZEƱ̬qHJ3z#{Ҍ5h]@G{+86Y"F3b)VwX>o"y>;b nyu*/כp7Vki^Zׂ24^M1k`"1XLfFb|fJbP ^ cWTEo цhF{Ux *Ү|(_QWUwaW}{N$"?eA3ȫWUR\:{Eg1Lc>~R ʽvsσ8e8K.S^uyo^% _.g?jM23E./Hx3[myܱ6iv*N%8`a݆u0sbcn1ST% 9Al{ 7{ql^fLV!Xd`L9zl`)P5QFI4E袸EE.&K F tNȪ"Ό:贰:%C%'{oUF!^/U' T6PpN!_`*MV"Xa*$RWQMAQ"'Sf WُIlc\Ɇ5BvJ.ܸ%wU(r-J͉*FR*7υ*;Q* NLCJIొGOU,<#>_ B'G6KCꧽΎXn'qE>"D1 D]͉v&;ll,g2[&ztlOayƙny覛nn1#a$1|v3ks2s3i2[3h8k7DZ"nq-/մ;]׵]{ gH{M -6>9 Q lNu*̲1~uk>t W^r%yk$g9\rw w'Ɉ[kbbI&̴BciAMd 㨫(b$G$'yAnB0%_)D1>4TLsM,6)@(lgU{iVj\3kq>ls oN^|1'[^Cux3+۳Gߟawb݀v96 XDځn;VArBI^ɂ?lbxKlD>㤨X5LOc<*]Dwi'H%}{kYŕ+6id UFۜ95k~+ߦ̜̦6 kĒ'3by;|M>< AGC3wyOμa9_q6tfSlZbIqW+w(n0^d={3FU/wD̵=ax7G-mRԳPjhMF 1D[ mpM+;+W>wcW>pjtL𹴽˹]}:Џp!5Ԍ0梿R3Ɇ2F C1ȎA?^v.ϸrݮG}v]Cds qf ?1K]u3>2Lg0pte .Я.qdf!]gd=2}&ce]Jƥuu:db.w8ۚdbuK})K4 ؒx]YFiE6-Ϙ62QilBl}"<%#r￴u*. iliU0:lwQ~;H0OibG(O=׶㩯H==u9w3' FDyP)UAʝܗvF*[鉌D'm)ms9aHik!>Hh+ -d4(oK"}*Ogg_`䵁Bپ5o*/z|?+i3??{gOlD }9'GbQHeT$Te%*#Ui)ј}U9ɪ,Ve#8*yUYn*j|ltMxڒu$;u'tC{c)6~u߳%k04P)mik=T| cMbc [#6תʠ)U /$"D!wPHߚQc_:jZ2eu+QB5r )Fql^;Pg01{u[؎;.n% xw\O.?P|p_ %.O]vwU\eJc+͜\t)%!_TDj"-!=pa(w<"%eόSH쩊dCA\E"#;2z7rFa%ލAo+!SYe)d*5d @.MGj`"Jʼnb~*^jӯj7|.;=%)HlϮpU+*].9R~Sv7>D*jk>8"pM 7$uCp%Mt MDlEL%"ƪsNMR!5Q N[Pxtn  1\w89$q9C +]6WMrֵks])\_H4|' 1X|F$HɅ1|va<|~U_矪 PY 1ʓ1PX\ZtF0.;9.t#{!4B9e*E8/"%Aa. Rb75zB8FwlW }5>g^ 7}m"6fk#-7;rg$CCD zxf5S#Fv;Y;(sxknhr%.У"%%9<*JtUf5FD;,ՑE RɤRɤKBS߿yOD*"5HD/`,!jWY'#T_zJj|:HwNک6H U$#鄄go3^^'U?D6՟U)XpFj,׎ fI@:HG:mY7Uxԛ"XaMXu5h&`fdYǒv;Jr*id`FIKV9#疡~1<f1 `4'Zs^_38C[z'uMz0#D#ލ_ Q(IX~j87w&m$X6h=i_}ziKN\n:t9D:tԉ.:J?QNGIPuJi@J[>@EʣzrWwcO^2WIVBc*%"D;'|*DdlB  S A?2nfm ~'wJD`!Bfm ~'wRx]Q=KA}3W.A?rIaeXbeEw'[#,`:3{&]ffd4e5XYLdq_m g1Mܪd;KkXGv-L³;f]k7,/mxu/aImJ|lC2f~7b##0e(ǣ|xS;H].uw kvzݯ2g#+_i{6Dd\ B  S A? 2+u[+D2䠀{#H`!+u[+D2䠀{#`@"!xTKkQILlNVLM 4}-bR7i@*V:#FA Uݫ.|JT0=Σv\8ɜ{99s!(8bQ!F+nW"#D _|j AXNHw)`_(߫3 N|5tYxFU1S]hCEeiŶU o~t;A]; q85u') 2#8AR#M0IֱHR f۪|&[~|0CaWgv{!DQ~қYo<<Dxj weh1G2z;l2 B{K+%qbkDd lB  S A?2>mf ?K`!>mf ? xuNAgg8vLl_@  Qh,lHl}; JckAa#XC /ogeL`苉D@$aEےdޗFS/qWDCBktvyZYpVm]T7uFR)Tug%hلP a31l6Нy!c('Fn\;yfP֮bNy{ /4X_"&\4y"tּTQ|ϩNcJ"f Yt1nBJ{،Q[ömbǒY\D^9O{  dn{ł\A;,!?AuPTAY>K(%_23lꁹYTkoMwś+:^Z52>Qf6F޻uXTBZ;J&LJ'^335΁ _ŽvԸ?,<;soEk֨fT(|)4#x"'YJ|uZ-+O1҅x㧹 ~.[֗Je3`0e?9̮?@ABCDEFGHIJKLMNOPQRSTUVWXYZ[\]^_`abcdefghijklmnopqrstuvwxyz{|}~ FRoot Entry` Y 0 FIX`\kDataU 6?  yWordDocument? %ObjectPool? c6\`\0_987407990 F6\6\Ole CompObj\ObjInfo "%&),-034569<=>ADEFILMPSVYZ]`adghknopqrstwz{|}~ FMathType Equation Equation Equation9q@ s=2vt<%2 FMathType 4.0 Equation MathTyOle10NativeD_996388059O F6\6\Ole CompObj ipe EFEquation.DSMT49qܰ%MU2GxDSMT4WinANSITimes New RomanSymbolCourier NewMT Extra!/'_!!/!"!APAE%B_AC_A %!AHA_D_E_E_A  tt== 8866,,000000 mm88 mm//ss==1100,,775500 ss  ObjInfo Equation Native  _987408444 F6\6\Ole 11 hh33660000 ss() FMathType Equation Equation Equation9q t=st=20 m340 m/s= 0.0588 s' PCompObj\ObjInfoOle10Native_987408610 F6\z>\Upda FMathType Equation Equation Equation9q 2v=st=40 m + 40 m5 s=80 m5 s PUpdaOle CompObj\ObjInfoOle10Native_987410165" Fz>\z>\Ole  CompObj!\ObjInfo# FMathType Equation Equation Equation9q 2v=st=400 m30 sPCancelOle10Native$_987410302 Fz>\z>\Ole 'CompObj (\ FMathType Equation Equation Equation9q 2v=Dt=40 m30 s%2PCancel؈D؈D FMathType Equation Equation ObjInfo!*Ole10Native+_987411292,$ F`G\`G\Ole .CompObj#%/\ObjInfo&1Ole10Native2_987417843@) F`G\` `\Equation9q 2v=s 1 +s 2 t 1 +t 2 =0.4 km + 0.667 km0.0667 h + 0.167 hOle 7CompObj(*8\ObjInfo+:Ole10Native; FMathType Equation Equation Equation9q D= (0.667 km) 2 +(0.400 km) 2 ;tanq=0.4 km0.667 kmc?_987413413. F` `\` `\Ole ?CompObj-/@\ObjInfo0B FMathType Equation Equation Equation9q v=0.778 km0.0667 h + 0.167 h=3.33 km/hhanges to Equation in C:\WorOle10NativeC_9874180493 F` `\` `\Ole GCompObj24H\ FMathType Equation Equation Equation9q t=st=400 km90 km/hCancel FMathType Equation Equation ObjInfo5JOle10NativeK_9874185951;8 F 4i\ 4i\Ole NCompObj79O\ObjInfo:QOle10NativeRd_987418855= F@p\@p\Equation9q` 5 m + 10 m2 sP&N FMathType Equation Equation Equation9qOle TCompObj<>U\ObjInfo?WOle10NativeX Dt=5 m - 10 m2 sPCancel FMathType Equation Equation Equation9q a=Dvt=-10 m/s_9874194246YB F@p\@p\Ole [CompObjAC\\ObjInfoD^Ole10Native__987419665G F@p\@p\Ole bCompObjFHc\4 sPCancel FMathType Equation Equation Equation9q a=v f -v o t=40 m/s - 00.5 s PObjInfoIeOle10Nativef_996388506LF`vx\@?\Ole iUpda FMathType 4.0 Equation MathType EFEquation.DSMT49q%MU2GxDSMT4WinANSITimes New RomanSymbolCourier NewMT Extra!/'_!!/!"!APAE%B_AC_A %!AHA_D_E_E_A CompObjKMjiObjInfoNlEquation Native m_996388553JQF@?\@?\ aa== vv ff22 "-vv oo22 22ss== 00"-((8888..00 fftt//ss)) 22 22((118800 fftt))ew  FMathType 4.0 Equation MathType EFEquation.DSMT49qOle uCompObjPRviObjInfoSxEquation Native yX<%MU2GxDSMT4WinANSITimes New RomanSymbolCourier NewMT Extra!/'_!!/!"!APAE%B_AC_A %!AHA_D_E_E_A  xx== vv 00 ++vv ff 22()tt;;tt== 22xxvv 00 ++vv ff == 22((118800 fftt))8888..00 fftt//ss ++ 00() FMathType 4.0 Equation MathType EFEquation.DSMT49qܬ%MU2GxDSMT4WinANSITimes New Rom_996388589VF@?\@?\Ole CompObjUWiObjInfoXEquation Native _987425822E^[ Fg\g\Ole CompObjZ\\anSymbolCourier NewMT Extra!/'_!!/!"!APAE%B_AC_A %!AHA_D_E_E_A  ss== vv 00 ++vv ff 22tt== 1166..66 mm//ss ++ 0022()33 ss()D FMathType Equation Equation Equation9q a=v f2 -v 02 2s=(2700 ft/s) 2 - 02(2.33 ft)ObjInfo]Ole10Native_987426255` Fg\g\Ole CompObj_a\ObjInfobOle10Native _987426672'e F \ \ FMathType Equation Equation Equation9q s=v 0 +v f 2t;   t=2sv 0 +v f =2(2.33 ft)0+2700 ft/s @xlExlEOle CompObjdf\ObjInfogOle10Native FMathType Equation Equation Equation9q a=v f -v 0 t=4 m/s - (16 m/s)2 schanges to Equation in ANSCHA_987427196j F/\\Ole CompObjik\ObjInfol FMathType Equation Equation Equation9q s=v f2 -v 02 2a=0- (16 m/s) 2 2(-6 m/s 2 )Ole10Native_987430733hro F\\Ole CompObjnp\ FMathType Equation Equation Equation9q a=v f2 -v 02 2s=0- (22.2 m/s) 2 2(40 m)orObjInfoqOle10Native_987430996t F\\Ole  FMathType Equation Equation Equation9q s=v 0 +v f 2t;   t=2sv 0 +v f =2(40 m)22.2 m/s + 0CompObjsu\ObjInfovOle10Native_987434504y F\\ FMathType Equation Equation Equation9q v f = v 02 +2as  = (-6 m/s) 2 + 2(-9.8 m/s 2 )(-40 m) Ole CompObjxz\ObjInfo{Ole10Native FMathType Equation Equation Equation9q s=0-(24.5 m/s) 2 2(-9.8 m/s 2 )n\Scan32._987434245m~ F\\Ole CompObj}\ObjInfoOle10Native_987440494w FĤ\Ĥ\Ole CompObj\ FMathType Equation Equation Equation9q s=v f2 -v 02 2a=0 - (80 ft/s) 2 2(-32 ft/s 2 )6.doc?ObjInfoOle10Native_987441211 FĤ\Ĥ\Ole  FMathType Equation Equation Equation9q v 0 = v f2 -2as  = (0) 2 - 2(-9.8 m/s 2 )(16 m) s\ANSCHAP6.doc?CompObj\ObjInfoOle10Native_987442275| Fb̤\`S椏\Ole CompObj\ObjInfoOle10Native FMathType Equation Equation Equation9q t= 2yg  = 2(-340 m)-9.8 m/s 2da_987442807 F`S椏\`S椏\Ole CompObj\ObjInfo FMathType Equation Equation Equation9q t= 2yg  = 2(-20 m)-9.8 m/s 2Upda FMathType Equation Equation Ole10Native_987443084 F`S椏\`S椏\Ole CompObj\Equation9q t= 2yg  = 2(-4 ft)-32 ft/s 2Upda FMathType Equation Equation Equation9qObjInfoOle10Native_987443192 F\\Ole CompObj\ObjInfoOle10Native_987488831 F@\ \ v 0x =xt=5 ft0.5 scel FMathType Equation Equation Equation9qOle CompObj\ObjInfoOle10Native   !"%()*-012589<?@ABCDEHKLMNOPQRUXY\_befgjmnoruvy| t=-v oy g=-30sin30 0 -9.8 m/s;t=1.53 sFiles FMathType Equation Equation Equation9q_987528633 F \ \Ole CompObj\ObjInfoOle10Native_987568696 F \@\Ole  CompObj \ t=-v oy g=-18.55 0 -9.8 m/s 2 ;t=1.89 setwork Associates\McAfee Virus FMathType Equation Equation Equation9qObjInfoOle10Native_987568828 F@\@\Ole  a=v f -v 0 t=(140 m/s) - (60 m/s)8 s=C:\Program Files FMathType Equation Equation Equation9qCompObj\ObjInfoOle10Native_987570867 F\\ s=v 0 +v f 2t=140 m/s+60 m/s2()8 s()WorxaDxaD FMathType Equation Equation Equation9qOle CompObj\ObjInfoOle10Native  a=v f -v 0 t=0 - 30 m/s10 s FMathType Equation Equation Equation9q s=v 0 +v f 2_987571046 F O \ O \Ole #CompObj$\ObjInfo&Ole10Native'_987579833 Fv)\?:\Ole +CompObj,\t=30 m/s + 02()10 s()on in C:\Wor FMathType Equation Equation Equation9q v= v x2 +v y2ObjInfo.Ole10Native/_987579964 F?:\A\Ole 3 = (60 ft/s) 2 +(80 ft/s) 2r FMathType Equation Equation Equation9q tanq=80 ft/s60 CompObj4\ObjInfo6Ole10Native7_996388760FA\A\ft/sPCancel FMathType 4.0 Equation MathType EFEquation.DSMT49q%MU2GxDSMT4WinANSITimes New RomanSymbolCourier NewMT Extra!/'_!!/!"!APAOle :CompObj;iObjInfo=Equation Native >E%B_AC_A %!AHA_D_E_E_A  aa== vv ff22 "-vv 0022 22ss== ((55 mm//ss)) 22 "-((2200 mm//ss)) 22 22((66 mm)) FMathType 4.0 Equation MathTy_996388759TFA\A\Ole FCompObjGiObjInfoIpe EFEquation.DSMT49q%MU2GxDSMT4WinANSITimes New RomanSymbolCourier NewMT Extra!/'_!!/!"!APAE%B_AC_A %!AHA_D_E_E_A  ss== vv 00 ++vv ff 22tt;;tt== 22ssvv 00 ++Equation Native J8_987597523 FK\K\Ole SCompObjT\vv ff == 22((66 mm))2200 mm//ss ++ 55 mm//ss[]b FMathType Equation Equation Equation9q v f = (5 m/s)   DC   !"#$%&'()*+,-./0123456789:;<=>?@ABnEGHJIKkMNOPQRSTUVWXYZ[\]^_`abcdefghijlopqrstuvwxyz{|}~ObjInfoVOle10NativeW_987598984 FK\K\Ole Z2 =5 m/s FMathType Equation Equation Equation9q` 2v=-3 m5 s;2P&NCompObj[\ObjInfo]Ole10Native^d_987605453 FR\R\Ole `CompObja\ObjInfocOle10Natived FMathType Equation Equation Equation9q t e = 2sg e = 2(4 m)9.8 m/s 2stExe=C:\Program Files_987605642 F[\@c}\Ole hCompObji\ObjInfok FMathType Equation Equation Equation9q t p = 2sg p = 2(4 m)2.45 m/s 2Ole10Nativel_987618686 F@c}\@c}\Ole pCompObjq\ FMathType Equation Equation Equation9q t=0.574v 0 4.9;t=0.117v 0XObjInfosOle10Nativet_987618924 F@c}\@͕\Ole w@(xKBQ=O}J2A)AU {)(C49- mKa[{=s?#0 }A +ЅpBqYpG"B2'#E! ?Ϝ'4B, a>L ,i'+5פʭ= ">ŖbɵnE[”B~fIʪ3E`|/A.pIL3&^Eb.-\ R٭9P\bCI>W]M7Qӌ}_B3c֕OF5Bge;K='=rP^W7{WHjmeǧl¡ 1ޭL l/GD>޷$YV#[GpchFd"ͤ~DP秉?,d.5jNpA<%Zm;Ť$f3Wl{yiD%~m-q,߻y^-%Ί?d1U0sޕRR*qFSfg]S^3b|*yp2E%ۅ7ޮ?7†u8ǼQG_]f[Dz5SPq~DdLlB   S A ?2S;EV?Ŷ'`!S;EV?ŶXu#xuR1O@~*HB-bU&Z1h' 1qar2767\YZ&׼c(R910}&geTI^ C4q1ãxr|?⍒4wlOAD T!Ey 3? #G\ڧ^mINI 7jO^ \CBcJa[tۂl|uZ{wS\Qɱ3jjTYHR""]N6r*HaArleV@F☆Y7sD@Hf /;^_7*q)aoc@zkDґIJ) 8xK QC,5^v)"~/boKDdlB  S A?2䅓A©[>& `!䅓A©[>& ~ (WxuQNA1$ B0^#1X'YPZ~Fϝ] ̾-B@].J#Rz Hq'rG' 'ס@jm S|7Wy+Uwkc5`VUjhюJanF& Y%0*r= ;MMPv}q 3F0Tkh8$,,eQt+I9$Ӿﴛ$jXe:F^K௣!WY7[)WL,HOWy C.!NSv;#RpeqIj.uL`Е`u@8ODdlB   S A ?2%x^ Gw`!%x^ Gwj w[xuQ=KA5\sh%M@ [-Lz/4bkgazKE2u]Dq=f̼y?Xr d9ބ(R$r*H)eYyKi>O$ƪr>w'y9ޘ%*2L+2Gb[*ŎFswL7hTA>>.a?8o7.A-rBWdNfm~rpf!}mx ӵ\Q~*ő5P0Me .䐗qH7u̵L9>Ͻ'/hZӣxDh0͙JTpfDdllB   S A ? 2Y@[k1a`!Y@[k1ؤ XhrxuJAϜn,(65!vZjH%6()[;-b)>vy_ 0˙of\ddEf1Z(E PD`$ΖĬ"E杏V!})Zp&`~.{}rwoβh:G!q60 / BNㇸB(MY:]w%)%c5\*҆uGO:*m<}OS^?tzuQŕUj٩,(T%oХ~ ҒrVgtrV5%vv9 ;%ս/n$\Dd B   S A ? 2M'I׷ `!M'I׷0 8dxR=KA%z`yDBchaRZ$‰g"- e *E ZX#6N py^лXz g- odBt?; ęFga5Dcԡ鋹%{lCWϡgC+qU3:=E9* *,d|QMU]ʵ:PU5󵞄U̕J~#N-[D:|ޚзOф8L6mg&5 Dp&Dd B  S A? 2-+нo EZ8٣C ]#`!+нo EZ8٣C`xTkAfvS4UMCrmA1)A$1V ^,Uz!=)fMJ7/{7o~0T!J3w:$ؘD&9#)!1Bڵ MP+Ria} 9729\|osi=!Ȉ_xHC/,U s|PVt1hLd BKq|QV׃UPٳA7ئc>kz*$RflC| 6}J%{KF89<̈l1ӛaN+Og58Mֽtkk]vWՏ ׫k`ٓI6?dg_Psy|~3 ` : K+J7E#0U{^_*ׅ:[0g֚1I^?(Fv"Ɉ"+Ψ3;; W!"v;;_(NgiaFbQMwBJ\}EVWB-\,UPVB<8UC툗-t25J!1m#$'7Hx> $eA&$$dq%ʂ ^HxK$5IjIv$^⒧=zעIwϢ3(}zY7B~W<Dd B  S A? 2e m^Ow '`!ze m^Ow8,`\HxUKSQstNnHR;9"`Y`4KBXY/؋ABz챇( !V~ݽsA|8|/*D(cp+|^J:Q)dD\5WózNT yr QE>O["PukI 9w# &cb~=z+MYS);Sg5-UQ7ш@T2 'ojgR(42`@ AenMF?5F!߉e9+ hHl~ :s BiҖVfZੀ|{YSøn i62֓)( ki P 9Dd3 B  S A?  2M"L*v}eaZ)\+`!!"L*v}eaZ$ ` PxTMLA~of mٖcD4PLoM@cK<@Rӭ "$xŘx'=.ތHL#!4PvHvf~޼y3> <4#aD(6 ).A],R#NV"jkX`<_.>,`2`:Zl0!uV|6v.$$Y V 9.ID~̢8h@=6¤l,y6&9pma\Z\(z& {E=?O\PC>YYv;qXRjP)ؤދsNW-oJ4C-6eXcI$xm~si'Ks/f.G[bFi]=<ѭdCqH!L=IQbm+_w^X7AYLW+e` DK{Haga=&Z='߂霰.oYrqO8S-'&@{ڑ7UgH.wU;h|SՔ`or˛]@ջ`:W]c 9OnNGMp9\MbHB*kut )\ĥssmj..YE U'/h®fZ?, M33T`4(i1$|ZZsʭVQ DdB  S A?2w͵ARgKI6S1`!K͵ARgKI6`(V'(+xOaǟmv BlKDq`[1i@H !.pI'p@..IyB7wy>>k fz61AFQk TZ!ݮNLE(& ."&v@6Na,R((Y V wf.e3g?r/F><~$% @0|b4 +/6CUHk310(|1.|!X.ն &}>%K/ɕRdM`/<6VK“o\J@vthZY/[ݤg-Ŗ,= GȝRvR]j _8QRV?`!^aG)jNێzM(:\u'IcC\SEk*mǘw)Ck*g799n6m]||Zt{ﺳT8!Dd B  S A?28",ADg,7`! ",ADg,, xSK@~RkI(_X!⯨ԡtԥCF[7AxwKM {rG t#@qdQHGzװ7Jz8F"ZP2b9RN&h4ՠ9i{/l劇+)J&Y;q7E4zJl-&dG_>a]۶-XN;/ܘtgT:P59O6@HU0$P6_|eԂ>ɲj6aO DE{`P3`aK 9d'.s==`{al<@jEeNMqUyzn(| 9W42ӓ%: Yq`c @,&gButg,A/XCdr1dwҽROzFAM"g*>thG~[b*[t ]r |WFDd B  S A? 2#T:6:Z 6'tu:`!T:6:Z 6'tuAxS=/Q؏Ya  Ȳ& ~[JFc%+dB/Y(D%zbz@t( l#b7s޽>4&#-BRE {%QBU!L{¢D+8rH0Μq3alxe,6ȧG(eQvYaJcW}H#]_ ;od>Wƀ!T)^ [p#;M?dr UF*Jeq5K0)N ĸ*bi H.(0/T'>ec$|guN:6bW bS ~kt\3lSr ]!7Aw=7(. :y+Ty*ןIh`,As OXXI*96$׭w$ꙫ7k"2 Dd@B  S A?2v:lAV{R<=`!J:lAV{vM((+x?LSA{ RK5*F0 01q+&%|ҤWVx  !LgeALxaB|5>}wdiPzD \ѐ1Iqd҂xkZ~D9W;aiہ5/\]D=ڃ9(GgvJ{_u B w>ܕCEx?gFSSrh9WӺ6\3SWөgRρOkTN;3!jșSKJX6A%y]y DdB  S A?2t}&x H NPH`!H}&x H N 0h+xkA{sqgrF#QX"]brHB R sE;BD6$\sh`!VJڀ73o#|߼yA9~zrz(HId&qTiB'G((0gWza=Nvxl|V{Zk /M)yũziw2htޢEcfzF6GN]kwT{;vTM!6@'kOfos[ ԩ]]79xVy&(M$].'%?S:}<>Ƃ.,,ISdzU+ٚtg3kXqZ JLZ+g[g@|NV*)٘.UM_Yi m}YdZܜPU˸.O/Ĺ8.AXw \o=y]oqo%>1koc`E蓷}wH4>ۊrY+BԫlDdL B  S A?2dYv _?`M@K`!8Yv _?`M"p(+xKQd״EX4{K!x(jI\$^{鱐?hޅR(A(AYy@,~޼wfޮ2!EzP&8YL0*d&Ĵ{moP]nonΨT Qv* ZE h8o\@; A0 *GgWV:?sHlDl:c*Zf_${rӞ M{^GN't+[AsVԶٍpyݜOI ϳEXm!C  #I%Dspec $uv&MRB:gIolʪK4_rM]>s]Ir>p,t(g˪Ae*E@̎OZ*[yRLΡ#o;}o{M.<-O.%GF-fL%kVDd8 B  S A?2Y-|T-t0 T5N`!--|T-t0 T (+xKQ۸&A-x\,[xȱǔB&?Bxh.\ R([ͼl@paa3k,"zsH^8'|Kb2 s.V}'}e=Y8dw}76:ݝUJYL%UI攵/F.B0 OkkkŠZ*[oVQ5;?S㜛9PDF9 G%,oN7B9l`m;2) yWb;Ős!҅C$"x΢w&Ir5e+3ir.z9" kdpWmʪK*4oLVW2vc^s1KfLLӣ͔u2Rb<ʂxS g2?M G oӯtkRzEp'mwZc'*9?mDdB  S A?2KHdmB'Q`!HdmB`G(+x=HPKMZcPX;8V*h+ -Hqsqpq\W'""Rp(8h|>j[ .!N+ RdM%2^BhTD-m>A':t2]Ti*1PW`J0)++ΠbFmR`ZAԨui^!36S*v-any"ʽY;F߳MO߭ }rvh^-D~l|XiIPm 4b2jRᏜ2xr}dg\m]u]:DpW#ǁFr^BD5R!/=Ɵԗ`~G2^]UFN;ЦɹC{OK~Q 2khyH$ux `9)¡vu׼Q>ުlI/8RRb`˧K0r/~fg\ƈuDdlB  S A?2ʐ4.CT`!ʐ4.Cb %xR=KAw%XR *-LN"L5XإK"~!.ofߛBݣ8`;G2ʈM AO*MB.O CF͋d-"p>|`7kN r,.UTJeԬ=&%dd%svܣE?K pk'aywgMY6s3H L")rCx|Κ! 13pQz߀ΔY\}0/ȺԸz$ݰ>cSg Cf"cJc~x˛rWNGM\mf nxL{PDd B  S A?2LH^JJ]D34 63f:4mf7yo?H-a$'7 @۶{|Sb< 7.C YjHZct}c/R֬GjC4W 5%BpjR]'}9LTcuc<4VVe_u~^\ PlE)DNxrtʆݷSYMk|?`&ɵڴ6{vֹj ^=&z5ݘ^oJAϽjי^\grՒ@_&EXÃD:-o:AMZ ВnQqu62s ? ;xO^Ѩsvci#5\]_`!Uҫ&y-5E>5\`%P#xOQgf=r^9-9  ),?" ${ RX0j XXx&F cb-űwfn!8#_0|u!^&DI(JEI}dzbosbu9 %7xѶx0W]' *yPWI: RuiWb1#6OK, ?7?s!Gu &qCvcv:}0Em/)g3he'UH%5S VLJlJ1g|j1I:Mr  yOEL-ٙd?\t֕Dd B  S A?2KWLNb a=%BKص5H|ٗbd]s=~) ?U/\k=e6B㿑iž̃ 2JvnP6ȗمd\ՖF=lȪx;R_1B: cÿ&(ɆƟw5nJ.HmރMeoi,tM5_+z@s,(~AL#D!>aLOoR}ݖ h+MJ@ w!- ^Đq(NwDd B  S A?2mg >rR)-IBe`!Ag >rR)-`X!Px1OA{wp'yX͙h" h f ${ќ1 f  gbcCca! Fyove)Mv37ogJMRh?Gz QR$+xN$ao0n8F#Pàwpݡtm-W;wvJӔLU4M+ģj]4[2l~G7:Jo]Auq- "~̛j&:g*t86RSxoIpȤ ^7up?E}K'UZOw@͸d/d̒vL2Y8t( r Mɶɜ%HYK(ۙ]"nBn{ql:v.otq_۵Vϲ^֘MfXoBưJծ3c>V8*U\b*%*I?8t^dL)y~kI 2ۓDͅN'ɑ·VDd'B   S A ? 2Z0$.t7gJ6Eh`!.0$.t7gJ@%xKK#Aǫcthw A|!z̲1Beɳ" h@dϠ<)8vuOOL  _G]5ⶐ1IzgYL!d~^=j5 K8 Q:ԉ粷Al}_.濧 i"u/BuuJ}LBZvhGߊ]7V*a+2,sŴETcj#Ao/jYV"vQ&mojmF'Iܩw:Y\P)ana@6Iš:inUzA QOX ȓT/SHm>S,euJM>& 5Dz?Ό9pt9T)S%`# aMwze>Ҧ<2Xr}&-ο"'M`d- ³(7€ n#w>={njdFD͍&;4qV>ʯ!vrtrn{fn^DdlB   S A ? 2C"1F5k`!C"1Fά (jxJAgfc,CD"-$D8Q%FҞ H`9paogۙCAOJ$D EQV M\TϚfk9$DQꫜ9 S} |0ŅxM%s7)fZHQ/n:Ｐ'&Wa7ʕk-g&H(&պ~('yge8+ ghD݂W֬ޥ-+rVIKpZFkeV!P=o%ZP&lζRѻGHTu;h!_KDd B & S A&? &22Ȉ_@ m`!Ȉ_@ + xTkAfvӦid7m(Z7krrmA1)A)mIjlJ Ez^,A( B438ԜfG g4 )EjŻIkp tX$o%#ΦWc[ Ipw%\8OIz&Þ^\HwpC!7 gJ5͛9R"4g#b.^zgun÷Dlve_p9o^U/5hZ:3f U>P_[Q%ԐaՍX7-Gk ۺ-Vm첪.͛`_[ɞY+\}N 0 &&>H6R+S=93/\B,,PLiRTg*UaDL+K2NdNmkLBKjUGOkJ$0M'%HAZ}^#Hio^2ZDqw)B>,G9RUG]qv7M'AYd)A=/[X[ 9 b &L3H!4VB L4Z 4!d\ ߐX! P(R޽'nG+y$N]+Z$ ˵Ŋ"~LVDd B ' S A'? '2|ڲ+ㅟԷLv0X[q`!Pڲ+ㅟԷLv0,(+xUKQ{Ӝ$_ f I. RMz2pk)6){Iz%z| =@bV=$6Z[,{~ιs1T441@g 6f 9ɚrK#)Us$_@RGd"IH[s:gxb"2;*i(?Bһ f?RIrXغ>[؏f)U(b=ndM'r3 d,7Fw3i|v(Cifz;֔mej&J)F˕i<&nA<_YC,ݦh:]y1b޸1rVmio k4lҜsf-{4w1rg{L>N6b8 y짊tB ܯx- |({}e͙)Ɠ-/fCU!+4 fY?o _Jy/ȞVώ6s`x8rth$|u#fNFgupK̎Sry;w\.KwХLBf(s,zv$>@N|NB#U e/;qzh2.:S iKqĹ(wH 4$Vze!R-*UYۊ>H4rh\`@yrk%Er 4,RDVbF~٫jY*k /`P떷w{qxlx"CN\(<Dd( B ) S A)?(2!֒縬AY8mu`!!֒縬AY8@1xtxS=KA/ -~Q FHZhaRLԈbD.(;; 6Bjϝۋ^ o߼y7^#@+ķ|#cann dE7\5<Ap)^`cԻzWKU> r%KI&Ui %; Ǿ[)LSaOF[rϾ+3oktbmVK#\õa=5ƥ&ھV"gV;?J\+[*e@UTjK-ËFv[?W2:7n@ǎBYvfz3&y8Yab9MhX;֝yW )@^ʱQR|.k)FIi +&^LCLdNdwJU 7DOwADd$lB * S A*?)2K2MBhi@8x`!K2MBhi@8HHD MxuQ=KAMNrXQl*"(pAVlҤ+;u$wIyo"jUЫ&Ux HyqM‚WR/d-pi-|_Zs;keW1f bCe6G2?5J}.k'q7~/nwA^óhfIԽ2L)H^;L)`dkei4iqE'!l+ؽO.؛mi!t1FLM&Df⤜դc%u>MDdB   S A ? 2J XTF%N$5&Iz`! XTF%N$5*@`\xKQƿ{(X   #m$>$]ۈB ؘ.E@6v ibLse ;w3 9w uyΑ1Mi .M^))岌z_z|NHljc#R6*[; 1A tURFa ;';0¥/60)*zWEɰC ۣw~$&wϿwA<ߥ =_BGp&ήK~b$(:>Xr"5Xr"HO>c|kl[S8Rt\#^^rMa[1&NY1ݏ GN>ldd^錆qE Mi  cɻY_ҫ>nn#;zNjLۿ,@#e_ňzoiB\@ Dd B   S A ?  2PJ!k 0,)}`!$J!k 0,`x=l@Ή7MLUUZ13@:EHt@,lt҅)702Vb`sw.UTز{( .C_H[zHCeY-$a!Pofbs{fq7c}elot[M JM%.*C9&fhE:8 _޾V?z_%3gix*W}9aߩ9OwlgSC/B4^gI.VÔjбZ2=Mxkɉ\01R'sH$_,?|-u3G\F[׻ý W;kI}S:>OZёdww})O,YK~Z'Sl4_Em-nʼn7aYkL6r"fF? BhYh K"o-A4_;=g3&Ҳ{Dd lCompObjx\ObjInfozOle10Native{d_987619028 F@͕\\ FMathType Equation Equation Equation9q` t=14,649v 0P&N FMathType Equation Equation Equation9qOle }CompObj~\ObjInfoOle10Native 0.574v 0 4.9=14,649v 0P' PUpda FMathType Equation Equation Equation9q_987620141 F\\Ole CompObj\ObjInfoOle10Native_987583787F_\'ȥ\CompObjeObjInfo t=0.5(2)v 0 32=0.03125v 0P' PUpda &FMicrosoft ClipArt GalleryMS_ClipArt_Gallery9q[[[ Results of Last Find ]]]D:\Clipart\TN00350_.WMF`p\vvv`pv'vvOlePres000L<Ole10Native1TablevSummaryInformation(< R  hl  l- "- "--8$X<FAFNGaHwJKNPSX_it~mX----$E'-:HNE----j$3"9FQZafknqsuwxxv sn b(W*O+LXITADLTWWVUSNH@4  ----j$3 -?Ucnw~!+4>GP]~dsgkghJtOe:q?^>a;i5p,s&ssqo ke\P<2// ) ----f$1pxw}%7FxPcWMZ8Y$TJC9."}s k!e7bKc]glpx----v$9 -?QcsgL3 xiXG5# (5|B{N~[hv----$rnorspmjfb]VMA3$$0 7<'>7?D?O=Z7f0p)v$wwxyzz{{| *43,)+16863/-/25752.,-/4;AHR]hs}q]I5  }jWF6'%.5Hg---?->$Q#$%(,06>FRUTR_asFvGLS\gs0Nl"5I\o(9K[~isvi`YNE>840- *(!'.%=#L"\ k{%- 5=1CAFPHaKsNPPMF:* #8KZdhlvveYT7W;22:MhiS?,tcSE91..y/l0\1I233344431{/d,N'<"    '.1469;}=k>X@F@4A"A@?=:70)#{yz}!,;J~YveioYyJ:*{zjn[gLc?`'][ZUI8$ ',.2??>=93,%!}"o#c$X$N$E$<#/  vi`YW&%! ----h$2bWY^fpz$.:HXhw tfXJq>KWbmx2Lf"1@P_o~",6@JS]~gwqomnimemam\nXpTrQtMxJ|FC?<838<B{GsMlTe\_eZhTmOrJxF~B>82#zgUB/zoe[QRSVYm\[_Ic7f4h1i.k,l%x   u"p%k)g-d1a6^;\AZRVcStPNLJHFS_ju $0<HT`kw}%/5;@FJ{OvRqVqWqXqYrYSLFA<72.*)'<$P"d wv hYK=. wlay/E\r "%(+, ,$-(.,//03172?3G3N4V5^6e6m6u5~5554320/(! %2@M[ixM_r}|zyyxxyzsnjgdbw`i]r[{ZZZZZ[[[ZYXUROOMLK{JsJlJdJ]J\I[HZGYFLIGLEy:X9W8W7W6X4\4a4e3j.d,],T-L;DJ?Z;k:{;<?BEGHIJKMPX`gpvz----P$&D"D,80+23468=DTdtn\J7  ~tj_TI@9x4e6Q8>9*::;::9875{3h0T.A+7*.(%%# !!! &+/2579;=}>l?\@KA:A*A@ ?=;850,&(+-0234(3:3M2_2q1/-+'&$"  &6F#W%g'x())****+, ,,#+/*;*G)S(_(f'l&r&x$w!u sqsw)6BNZepz$;* rbQ>*#-73.)$#"!!!"#$%(,17:>CHHHIJWdoz *;L]m}zjYJ=2*$ &5D D"----x$:A5)  %(*u*c(Q$B!3# wi&>Wn %2@A----f$1GVdq|iV~Dv3l#aTEMTZ`bce f ea[UNG?7.%#2@N\ht~ "+4=G----$vt~{wrle]UH</# }tkbmmnop}$5HNSX\`cfii~glb\YNGWHVIUISJRLKMJPJSJVJUDR>O8J3E-@(:"5/)"    $'+/421/-----% *5@JS \c#j/q!>,E6W----($2,2-2/2011/3,4(5%5'4'3(0).0)1)1)2*2,---- $1110//.--),.01----8$$& ' ) * + ,--+*'$$#"!   !$----"$787642000345677----($\OA3% $2@N\\----n$5VWUXTYSZR[C_3b#eggfc^\ZXWVUUVWZ\_`abcke 6\ZWSPMJIJSX[\[/ZBWUTUTVUVVVW---- $@h<x6-" yj\M?0""1@O^m|(w%q!mjgeb_\XURvObMNL;L'LORX_`bcc{eQNKHFDBA#@5AGAYBkC}DEFFFGHIKLMN PQQ R'R-R4S:T;W<Y=\<_@h----($ qaP@0 0@P`p ---- $iRi----"$:::97  # . : :----0$ ' >-?:?G@SB`DlFyIMRe}----$/ARwbnraSC2 wld\wVjP]LOJAJ2M$M#L#K"J!?$4&)'()((&(+.12223467741,'"J[H@:1'!# #"# .8BJRY^ ee"g6kHrZzjy%6BMW~`shho[tMy?y>y <:99ILNPRYaju,BF$H,----&$&<"M#L$J$G$E BBCD75 6"7$8&;&<----,$     ----d$0/6<:7-+)(*+.16?@@@A@@@?81)"#)/----$ ----$ b^]\ZYYYXXbb----&$''()*,,+,'# "$'----x$: ",58:;;;;;;9742/, '! yndZP\gs} ----0$ zrkd]VX\afmt} ----z$;L|vq}myjuhoffdXaF^4]!\\^bkrvwwww&x1x<zF|O~\dgffhjkie[L----t$8ZZ\]`c fimqt"x%{(}-3;DK~Q|V{[{_{c}hqx|~f~u}tzqvnpllljlfl^mXnSnNoIoCo>o9m3k-h&da] [YYZ----X$*_n*o(p"pmic [RJC><=AD E@3    xf_--vv_>$oe{sv7bb(PbEP[[[ Results of Last Find ]]]D:\Clipart\TN00350_.WMF pub98bal.cag Oh+'0 ( D P \ ht| Chapter 2 hapPaul E. B  S A? 2$k"Vkb6;e`!$k"Vkb6;erxR;KABrh&DK0!DKS$til;[`q`#X`i{~3;7! 8? +"D%RFYdH3g3ZIdax)~ʞQKҰF}YlP_A2ʚ/RGas51#[:%B ح=qZySt "v]ty\ GpƼfc\1vYrJ޷)ޜԸ !rgH:r&i4(Z1_wbk*"Sz8nfsΦ_G@3~ز8aY4))_XAՔې[ lڤR*~?xDDd8B  S A?2eG Қ~՚UZIjﱨ+-y.NdN(v ;B<:+@2YMO590K,@WVsjaexgϐsڡXMӝ $T32PIOWtDd8 lB  S A?2)/mF 7!͕Y`!)/mF 7!͕bxJAguAB"\ .%$(i$hew<x%{1ݙg@#ɧd%Daa̷!S粨#ynm ! _C8O3:jQl,2UZk Y+ܪzHN[Fnް.J;9U+O]#)coI"p4cyD5@E,Eh^#2Mkietw TU4 "{ &AژTD\|HELr^s(RW񊼰4P$&-nD@ .#r(y;".+ȷ!-Vb5<_w>v4r(Dd<  C A? 2' O9Ȕ'DC'7j`!' O9Ȕ'DCפ<d'x{VDzug``apK !h]w[7w֦]]]j2*RNz hD3ۍt>ĈF>>?1cF4sQӧ}aYljț^E!jzҫ~^ULaW[0u]zCOxM#o {pma͇o4}|2w###ITK\lse/]Qp8888P>s< g`(hl!|W&-3qŔ9SMk\3pc3/|0?NB|;)Tdӑ%J򽒝0;v&:Z-ڞ(eܖ(f; Fd Rr<8.{6ֆ8i86lD#ݤFuܧv~S=x0C1c0S110^ng<:|$E eB (&PjFcɂzUŢ|uE W.Fk "C,j{[q.;m{WG͏6-ؘg Fw}:G*뮀2.==^Ιv''3q0٤hL|gb!)Fgbyf2XkaY' .7ԯ^j`/9`<^Nv{-L?O@ &"?&# (9crs+x{m w:GX,V %;JJ!"o"&o$d~HC$H}|Nv$G ~#ZsJtI396k!E+w_KV!DZ|NYPYDYꧠ7-:I %@>'C{Qh$JrŅ!Q~uesX^w;UnVXcn:khddDA%t,/=w=w67ly|wUo }Ut1 qu4r7ԤGMf0.&/DK\2ucq]crKM|( 6>DlM63\f `lCmm4ǧɹȵF5;:k%C G>hAr9#ؕUlW#Į%oD!f`vϜn=#(cRΣC4{{p9gO1{hg#Fb'9}mFTsXbL>d/hDv{إG] {}2'Ss0Ys5ml,֛4Xcb & (l3,1r% :1ʸ;r-u4>HGڒK$+VI"A%WJ]p>J=Dy4GKfՕddԥgz%z&dyRSVI,cd,cUߋr@Ju]2R@ݖ*ꮄ]=PdM֨Y$vz.'Co ^hz$%^&E,IS=D:Wwaэe)t٨K~]XPy'[b䐌&Rd&l2 ^ƚt2ˤe&3%Ҥ~ q}9>`- m gI[QleiiIo[S0Y@l5(nۢ攸^*Ŕ=C6xW.yNbw3̖c -No3 ^xf}hMEcf1R.٢8gk3d}v1y;ѓ~'1ŞEG=h{viUahzGFf'v+nʹ8v#f105i }#db2!51AbBGBP<֡8Ac·A: Q\gBtB|VFsOU4% XX7'8qUeWgXua8jc].ggcv;63|Z!OH'>O $K'FHԑ/E My# ,R]fJsP/Y,#@e֊jÿAu_6-[ $jIm18ğu$'t $Tº-|&jd"WS9$^ c_y6-[ΨrX%v)YIexuBcҁ\؀s˩WjS;6y%LQqZAona>T*B}|/ $C&\ W$> 4O(m$y$ J4"uer-)3l)YBFEȑj+ɱ6*N+1[;C&Nr1^s,;rݟFA,RAVK̕''#Yb<*8kKXW֒nDO/7h4`MWYvʸڗ*1}86[Όv-H쐲#EuZ cܮƌ<26c<#>/F2^LI:gG⢇x"_]yڰvl!]\sk(G\}겎 upe*ӈ QȕaYZ"]Y93p䩫%EHLf܉a}K 3\er@y|'9^zG}̽%*Pgk(MD7=1:Vr:|3 T2ABQ"i'+e›-¨$乜h$Py%͙wgf?1qCݐ guDٌh'-FB5ɸwj5 [f=Fgȭp(A1[F5AњQajbUUD8*,ǮQ^pOj(xz*RyȢ#/#VqGBGg} ֯0BX-cJN$uVeY{[ZFQèA_rSOfR=uCјwXFH]FrS׼CKƊ.\qc+6D:Jn!؏DjjH@hҘL5FlG>x/>v{\Ù1cע^6W&u }d&uyMT0YD/9|BsETn9L6`)ST%&cMf^؂ҖJ|!hb1sqJ~ ׈ZEƱ̬qHJ3z#{Ҍ5h]@G{+86Y"F3b)VwX>o"y>;b nyu*/כp7Vki^Zׂ24^M1k`"1XLfFb|fJbP ^ cWTEo цhF{Ux *Ү|(_QWUwaW}{N$"?eA3ȫWUR\:{Eg1Lc>~R ʽvsσ8e8K.S^uyo^% _.g?jM23E./Hx3[myܱ6iv*N%8`a݆u0sbcn1ST% 9Al{ 7{ql^fLV!Xd`L9zl`)P5QFI4E袸EE.&K F tNȪ"Ό:贰:%C%'{oUF!^/U' T6PpN!_`*MV"Xa*$RWQMAQ"'Sf WُIlc\Ɇ5BvJ.ܸ%wU(r-J͉*FR*7υ*;Q* NLCJIొGOU,<#>_ B'G6KCꧽΎXn'qE>"D1 D]͉v&;ll,g2[&ztlOayƙny覛nn1#a$1|v3ks2s3i2[3h8k7DZ"nq-/մ;]׵]{ gH{M -6>9 Q lNu*̲1~uk>t W^r%yk$g9\rw w'Ɉ[kbbI&̴BciAMd 㨫(b$G$'yAnB0%_)D1>4TLsM,6)@(lgU{iVj\3kq>ls oN^|1'[^Cux3+۳Gߟawb݀v96 XDځn;VArBI^ɂ?lbxKlD>㤨X5LOc<*]Dwi'H%}{kYŕ+6id UFۜ95k~+ߦ̜̦6 kĒ'3by;|M>< AGC3wyOμa9_q6tfSlZbIqW+w(n0^d={3FU/wD̵=ax7G-mRԳPjhMF 1D[ mpM+;+W>wcW>pjtL𹴽˹]}:Џp!5Ԍ0梿R3Ɇ2F C1ȎA?^v.ϸrݮG}v]Cds qf ?1K]u3>2Lg0pte .Я.qdf!]gd=2}&ce]Jƥuu:db.w8ۚdbuK})K4 ؒx]YFiE6-Ϙ62QilBl}"<%#r￴u*. iliU0:lwQ~;H0OibG(O=׶㩯H==u9w3' FDyP)UAʝܗvF*[鉌D'm)ms9aHik!>Hh+ -d4(oK"}*Ogg_`䵁Bپ5o*/z|?+i3??{gOlD }9'GbQHeT$Te%*#Ui)ј}U9ɪ,Ve#8*yUYn*j|ltMxڒu$;u'tC{c)6~u߳%k04P)mik=T| cMbc [#6תʠ)U /$"D!wPHߚQc_:jZ2eu+QB5r )Fql^;Pg01{u[؎;.n% xw\O.?P|p_ %.O]vwU\eJc+͜\t)%!_TDj"-!=pa(w<"%eόSH쩊dCA\E"#;2z7rFa%ލAo+!SYe)d*5d @.MGj`"Jʼnb~*^jӯj7|.;=%)HlϮpU+*].9R~Sv7>D*jk>8"pM 7$uCp%Mt MDlEL%"ƪsNMR!5Q N[Pxtn  1\w89$q9C +]6WMrֵks])\_H4|' 1X|F$HɅ1|va<|~U_矪 PY 1ʓ1PX\ZtF0.;9.t#{!4B9e*E8/"%Aa. Rb75zB8FwlW }5>g^ 7}m"6fk#-7;rg$CCD zxf5S#Fv;Y;(sxknhr%.У"%%9<*JtUf5FD;,ՑE RɤRɤKBS߿yOD*"5HD/`,!jWY'#T_zJj|:HwNک6H U$#鄄go3^^'U?D6՟U)XpFj,׎ fI@:HG:mY7Uxԛ"XaMXu5h&`fdYǒv;Jr*id`FIKV9#疡~1<f1 `4'Zs^_38C[z'uMz0#D#ލ_ Q(IX~j87w&m$X6h=i_}ziKN\n:t9D:tԉ.:J?QNGIPuJi@J[>@EʣzrWwcO^2WIVBc*%"D;'|*r(Dd<  C A? 2' O9Ȕ'DC'`!' O9Ȕ'DCפ<d'x{VDzug``apK !h]w[7w֦]]]j2*RNz hD3ۍt>ĈF>>?1cF4sQӧ}aYljț^E!jzҫ~^ULaW[0u]zCOxM#o {pma͇o4}|2w###ITK\lse/]Qp8888P>s< g`(hl!|W&-3qŔ9SMk\3pc3/|0?NB|;)Tdӑ%J򽒝0;v&:Z-ڞ(eܖ(f; Fd Rr<8.{6ֆ8i86lD#ݤFuܧv~S=x0C1c0S110^ng<:|$E eB (&PjFcɂzUŢ|uE W.Fk "C,j{[q.;m{WG͏6-ؘg Fw}:G*뮀2.==^Ιv''3q0٤hL|gb!)Fgbyf2XkaY' .7ԯ^j`/9`<^Nv{-L?O@ &"?&# (9crs+x{m w:GX,V %;JJ!"o"&o$d~HC$H}|Nv$G ~#ZsJtI396k!E+w_KV!DZ|NYPYDYꧠ7-:I %@>'C{Qh$JrŅ!Q~uesX^w;UnVXcn:khddDA%t,/=w=w67ly|wUo }Ut1 qu4r7ԤGMf0.&/DK\2ucq]crKM|( 6>DlM63\f `lCmm4ǧɹȵF5;:k%C G>hAr9#ؕUlW#Į%oD!f`vϜn=#(cRΣC4{{p9gO1{hg#Fb'9}mFTsXbL>d/hDv{إG] {}2'Ss0Ys5ml,֛4Xcb & (l3,1r% :1ʸ;r-u4>HGڒK$+VI"A%WJ]p>J=Dy4GKfՕddԥgz%z&dyRSVI,cd,cUߋr@Ju]2R@ݖ*ꮄ]=PdM֨Y$vz.'Co ^hz$%^&E,IS=D:Wwaэe)t٨K~]XPy'[b䐌&Rd&l2 ^ƚt2ˤe&3%Ҥ~ q}9>`- m gI[QleiiIo[S0Y@l5(nۢ攸^*Ŕ=C6xW.yNbw3̖c -No3 ^xf}hMEcf1R.٢8gk3d}v1y;ѓ~'1ŞEG=h{viUahzGFf'v+nʹ8v#f105i }#db2!51AbBGBP<֡8Ac·A: Q\gBtB|VFsOU4% XX7'8qUeWgXua8jc].ggcv;63|Z!OH'>O $K'FHԑ/E My# ,R]fJsP/Y,#@e֊jÿAu_6-[ $jIm18ğu$'t $Tº-|&jd"WS9$^ c_y6-[ΨrX%v)YIexuBcҁ\؀s˩WjS;6y%LQqZAona>T*B}|/ $C&\ W$> 4O(m$y$ J4"uer-)3l)YBFEȑj+ɱ6*N+1[;C&Nr1^s,;rݟFA,RAVK̕''#Yb<*8kKXW֒nDO/7h4`MWYvʸڗ*1}86[Όv-H쐲#EuZ cܮƌ<26c<#>/F2^LI:gG⢇x"_]yڰvl!]\sk(G\}겎 upe*ӈ QȕaYZ"]Y93p䩫%EHLf܉a}K 3\er@y|'9^zG}̽%*Pgk(MD7=1:Vr:|3 T2ABQ"i'+e›-¨$乜h$Py%͙wgf?1qCݐ guDٌh'-FB5ɸwj5 [f=Fgȭp(A1[F5AњQajbUUD8*,ǮQ^pOj(xz*RyȢ#/#VqGBGg} ֯0BX-cJN$uVeY{[ZFQèA_rSOfR=uCјwXFH]FrS׼CKƊ.\qc+6D:Jn!؏DjjH@hҘL5FlG>x/>v{\Ù1cע^6W&u }d&uyMT0YD/9|BsETn9L6`)ST%&cMf^؂ҖJ|!hb1sqJ~ ׈ZEƱ̬qHJ3z#{Ҍ5h]@G{+86Y"F3b)VwX>o"y>;b nyu*/כp7Vki^Zׂ24^M1k`"1XLfFb|fJbP ^ cWTEo цhF{Ux *Ү|(_QWUwaW}{N$"?eA3ȫWUR\:{Eg1Lc>~R ʽvsσ8e8K.S^uyo^% _.g?jM23E./Hx3[myܱ6iv*N%8`a݆u0sbcn1ST% 9Al{ 7{ql^fLV!Xd`L9zl`)P5QFI4E袸EE.&K F tNȪ"Ό:贰:%C%'{oUF!^/U' T6PpN!_`*MV"Xa*$RWQMAQ"'Sf WُIlc\Ɇ5BvJ.ܸ%wU(r-J͉*FR*7υ*;Q* NLCJIొGOU,<#>_ B'G6KCꧽΎXn'qE>"D1 D]͉v&;ll,g2[&ztlOayƙny覛nn1#a$1|v3ks2s3i2[3h8k7DZ"nq-/մ;]׵]{ gH{M -6>9 Q lNu*̲1~uk>t W^r%yk$g9\rw w'Ɉ[kbbI&̴BciAMd 㨫(b$G$'yAnB0%_)D1>4TLsM,6)@(lgU{iVj\3kq>ls oN^|1'[^Cux3+۳Gߟawb݀v96 XDځn;VArBI^ɂ?lbxKlD>㤨X5LOc<*]Dwi'H%}{kYŕ+6id UFۜ95k~+ߦ̜̦6 kĒ'3by;|M>< AGC3wyOμa9_q6tfSlZbIqW+w(n0^d={3FU/wD̵=ax7G-mRԳPjhMF 1D[ mpM+;+W>wcW>pjtL𹴽˹]}:Џp!5Ԍ0梿R3Ɇ2F C1ȎA?^v.ϸrݮG}v]Cds qf ?1K]u3>2Lg0pte .Я.qdf!]gd=2}&ce]Jƥuu:db.w8ۚdbuK})K4 ؒx]YFiE6-Ϙ62QilBl}"<%#r￴u*. iliU0:lwQ~;H0OibG(O=׶㩯H==u9w3' FDyP)UAʝܗvF*[鉌D'm)ms9aHik!>Hh+ -d4(oK"}*Ogg_`䵁Bپ5o*/z|?+i3??{gOlD }9'GbQHeT$Te%*#Ui)ј}U9ɪ,Ve#8*yUYn*j|ltMxڒu$;u'tC{c)6~u߳%k04P)mik=T| cMbc [#6תʠ)U /$"D!wPHߚQc_:jZ2eu+QB5r )Fql^;Pg01{u[؎;.n% xw\O.?P|p_ %.O]vwU\eJc+͜\t)%!_TDj"-!=pa(w<"%eόSH쩊dCA\E"#;2z7rFa%ލAo+!SYe)d*5d @.MGj`"Jʼnb~*^jӯj7|.;=%)HlϮpU+*].9R~Sv7>D*jk>8"pM 7$uCp%Mt MDlEL%"ƪsNMR!5Q N[Pxtn  1\w89$q9C +]6WMrֵks])\_H4|' 1X|F$HɅ1|va<|~U_矪 PY 1ʓ1PX\ZtF0.;9.t#{!4B9e*E8/"%Aa. Rb75zB8FwlW }5>g^ 7}m"6fk#-7;rg$CCD zxf5S#Fv;Y;(sxknhr%.У"%%9<*JtUf5FD;,ՑE RɤRɤKBS߿yOD*"5HD/`,!jWY'#T_zJj|:HwNک6H U$#鄄go3^^'U?D6՟U)XpFj,׎ fI@:HG:mY7Uxԛ"XaMXu5h&`fdYǒv;Jr*id`FIKV9#疡~1<f1 `4'Zs^_38C[z'uMz0#D#ލ_ Q(IX~j87w&m$X6h=i_}ziKN\n:t9D:tԉ.:J?QNGIPuJi@J[>@EʣzrWwcO^2WIVBc*%"D;'|*                              } o m l k [ W V U T S P M ' $ #              } |   y "    !"#$%&'()*+,-./0123456789:;<=>?@ABCDEFGHIJKLMNOPQRSTUVWXYZ[\]^_`abcdefghijklmnopqrstuvwxyz{|}~%18<AIQZeloru}%(/Pqwz}      !"#$%&'()*+,-./0123456789:;<=>?@ABCD [(@(NormalCJmH <A@<Default Paragraph Font, @,Footer  !&)@& Page Number,@,Header  !4O"4 Default TexthnH   !"#$%&'()*+,-./0123456789:;<=>?@ABCDEFGHIJKLMNOPQRSTUVWXYZ[\]^_`abcdefghijklmnopqrstuvwxyz{|}~%18<AIQZeloru}%(/Pqwz}a        !!""##$$%%&&''(())**++,,--..//00112233445566778899::;;<<==>>??@@AABBCCDDEEFFGGHHIIJJKKLLMMNNOOPPQQRRSSTTUUVVWWXXYYZZ[[\\]]^^__``aabbccddeeffgghhiijjkkllmmnnooppqqrrssttuuvvwwxxyyzz{{||}}~~EFGHIJKLMNOPQRSTUVWXYZ[\]^_`abcdefghijklmnopqrstuvwxyz{|}~      !"#$%&'()a7BPPPSR &/i!$&J*'-s03O68;X?BFKN~SVZH^_`acee58:;<>?ABDEFIJLMOPRSTVY\_abdghikx{ *t"d(V.55;8BEEG:HKaS!Z`bbbbc1cNckcc ddeoee69=@CHKNQUXZ[]^`cfjlmopqrtuvyz|~P"+?Wb3ccfee7GWensw}2DF 24Tfh  5 G I  Ldf.0Rdfhz|Vhj  :LNPbd }&&&@.R.T.2&2(2=2O2Q25 6 6&686:6@@@@@@G7G9G\GtGvGH,H.HIIILLLLLLTZfZhZZZZZZZ_\q\s\a:::::::::::::::::::::::::::::::::::::::::::::::::7>BILS!!/KMPln::   O"$IiA7叴 2$2ǎGwZ! v2$'[])f.y6RU2$ O9Ȕ'DC') 0e0e     A@ A5% 8c8c     ?1 d0u0@Ty2 NP'p<'pA)BCD|E||@V l  !"#$%&'()*+,-./0123456789:;<=>?@ABCDEFGHIJKLMNOPQRSTUVWXYZ[(  `  0? ` Y 0? r U 6?W r S 6?W ` 7 0? ` / 0? |`  0? s`  0? F`  0? E`  0? l  0? l  0? l  0? `  0? `  0? ` p 0? fB q 6D? ` r 0? 3` s 0? fB t 6D?fB u 6D?qv@ -('<7  ~ } 6$?Rn |5&<7 $~ |  6%?R -:&j/F %2 w BTCENGHZIyQ jJ?R TtTty`Tty`T1&5&B x  HDjJ?R@/&@/G~B ~  BD?R#n5$|5~B   BDjJ?R@/ 2~B   BDjJ?R&@/& 2~B   BD?R( 1('1l2   0?.R j/`  0?  fB  6D? fB  6D? u`  0?  fB  6D?^`  0?  @ *v '   ~   6?VF# >%  ~   6"?V* ' "~   6!?Vv ,& , !~   6?V " $l ~   6?Vn f" ~   6 ?Vj !*  ~   6?VN! F#  ~   6#?V% ' ! #~   6&?V   &~   6'?V$ 'B   HDjJ?V6 %6 B  HDjJ?VD $r2   6?V>r2   6?V | er2   6?V% V&| B  HDo?Vn %~B   BD?V"$" x   0?l$^& `  0? fB  6D?lfb  @ 6jJ?`2  0?`2  0 ? `2  0 ? rB  BD1?rB  @ BD1?`   00e0e    BCDEF A@  5% 8c8c     ?1 d0u0@Ty2 NP'p<'pA)BCD|E||gt~MgW@  xB  @ HDo? fB  6D?`  0? fB  6D?"D`  0?  `  0? !`  0? #`  0? %fB  6D?$fB  6D?&`  0? (`  0? '`  0? )`  0? *`  0? ,`  0? .fB  6D?+ fB  6D?-`  0? /fB  6D?0`  0? 1 `  0? 3fB  6D?2`  0? 5`  0? 4`  0? 6`  0? 7`  0? 8 fB  6D?:`  0? 9`  0? ;`  0? <fB  6D?=`  0? >fB  6D??`  0? @`  0? A`  0? CfB  6D?BfB  6D?D`  0? G`  0? H`  0? IfB  6D?J`  0? K`  0? PfB  6D?Q`  0? Mr  6*? L *rB  BD1?Or  6? N fB  6D?S`  0? UfB  6D?T`  0? R`  0? W`  0? VfB  6D?X`  0? Y`  0? Z`  0? [`  0? \fB  6D?]`  0? ^`  0? _fB  6D?``  0? a`  0? bfB  6D?c`  0? e fB  6D?f`  0? h`  0? gfB  6D?i `  0? k `  0? jfB  6D?l`  0? m`  0? o`  0? n`  0? p`  0? qfB  6D?r`  0? t@ f> ' ( ux $  0?%6 '  x #  0?"%> &  x "  0)?fv B  )l2   0? n ~B   BDjJ?b  l2   0?% &n  2   B2TENH0EQ ? `T2TN`T2TN`T2TN`Tb. ,& xB   <D?,& ,&t ~B % B BD?T< ,&< x '  0? " ` ) 0? v` * 0? wfB + 6D?xfB , 6D?z` - 0? y` . 0? {` 0 0? }` 1 0? ` 2 0? ` 3 0? ~` 4 0? ` 8 0? fB 9 6D?` : 0? ` ; 0? ` < 0      !"#$%&'()? ` = 0? ` > 0? ` ? 0? fB @ 6D?` A 0? ` B 0? ` C 0? ` D 0? fB F 6D?fB G 6D?r T 6?W r W 6 ?W  r V 6?W f J 6?WN M  S A ?WlB N @ <D?WxB O HDjJ?W N P  S A ?W lB Q @ <D?W xB R HDjJ?W ` Z 0? r [ 6 ?   fB ] 6D?@ zD.)r4 p  m  < ?X %.(t0  rb ^ B 6?X00)r4 r2 `  6̙?X%0&1 r2 a  6̙?X ^2!h3 B b HDjJ?X&0'p1 ~B c BD?X'f0<)0~B d B BD?X!/(l2 ~B e  BD?X(.0)f0B f B HDjJ?XV2@!3~B g  BD1?Xh%/r&2xB h  <D?X b1!4 ~B i BD?X 2 Z3 ~B j BD?Xz/%2  k  < ?X #D.r&/   l  < ?X 0!1   o  <? v%^2(3 ` q 0? ` r 0?  fB s 6D? ` t 0? ` u 0?  fB v 6D? @ '*,-  x   0?2!(&T* ~   6 ?)P+ ~   6?Y#^+&- ~   6?Y^'#J) ~   6?Y:&+*,- ~   6?Y+!- r w  6?YJ*)+ tf t0 2 z 3 Y pX)"!*r2 x  6? t0 2 y  <( ? 01 (tf t0 2 { 3 Y  't)( +r2 |  6? t0 2  }  < ? 01 xB ~  <D?Y4 *4 + xB   <D?Y'*'+ B  B HDjJ?YJ*b* B  B HDjJ?Y %8*4'8* B   HDjJ?YJ"0,B$0, ~   6?Y$'*J) `  0? `  0? 2 @ P> (*  x   0 ?  l   0?l$ (  l2   0? r l2   0?> 2 l2   0? :2 L !F#&  $6 & l2   0?.""&l2   0?"8#&l2   0?##&l   0?!FF# l   0?F##rB   6D?$  rB   6D?% %  x   0 ?P   x   0 ?# (* ~B  BDjJ?% &  x   0 ?#> j(  xB   <D? " x   0 ? : "n  `  0? fB  6D?`  0? `  0? fB  6D?@ f" ):&  x   0 ?`' ) r   6?ZP$%$ r2   6̙?ZH&&: r2   6̙?Zd& $ '$B  HDjJ?Z&"&P$ ~B   BD?Z&:&" ~   6 ?Z('p#(>% xB   <D?Z#^$&^$ ~   6 ?Z4$$6':& x   0 ?f"&, rB   6D?#H&`  0? @ ," D'R  x   0?~#8D' x   0?$!. $ x   0?,"R xB  <D?\!B\! rB  6D?N!% xB  <D?\! \!BxB  <D?" " 2   BC)aE$GHHuI`TQ ? )aY)aY`T`T)aY`T`Tj!" " rB  6D?" % xB  <D?""xB  <D?$ $p rB   6D?$$`  0? `  0? fB  6D?`  0? fB  6D? @ t0*N6  x   0?# 2)3 ~   6?[!r4"%6 ~   6?[v%4*26 ~   6?[t4N6 ~   6?[0z2 ~   6?[ 2::4 r   6?[Td4(4r2   6̙?[d&3(,4~B  B BDjJ?[&4&r4~B  B BDjJ?[ '4'r4 ~B  B BDjJ?['4'r4~B  B BDjJ?[|'4'r4~B   BD?[3&3B  HDjJ?[13f2   s * ?[1T#3B  B HDjJ?[$3&3r2   6?[8#3#4xB   <D?[4(5 xB   <D?[`'4`' 5 N t0*N6   x   0?!r4"%6 x   0?v%4*26 x   0?t4N6 x   0?0z2 x   0? 2::4 l   0?Td4(4l2   0̙?d&3(,4xB  B <DjJ?&4&r4xB  B <DjJ? '4'r4xB  B <DjJ?'4'r4xB  B <DjJ?|'4'r4xB   <D?3&3~B  BDjJ?13`2   c $ ?1T#3~B  B BDjJ?$3&3l2   0?8#3#4rB   6D?4(5rB   6D?`'4`' 5`  0? `  0? dB S  ?_Pw     ]RS;H 3 4 (  dJKPQTU@A~ fzt`tHhA !!!!##b$%I%%n& ''()z)|))W*G,,#-1.W002<2d2f23344K55$6%66+7l777B889G::+;p;;<Q<<<8>>@BDVEWEXEYEZE[E\E]E^E_EFFGUGGCHEH_J`JJLL M MaOPPQARRR4TwTTiVVrXXGYZZ[\]ap ^tq ,"tt H#tr :tu H#ts |7:t &'! t  t xt !~ t #t TNt d#t t F t :#t d#t z)Kt t xi~ 7t   t >'t b t ~ #4!t L" t B pt t b!Lt +:t y/t t 8+t t lf t VH#t Lnt "t t #t Qst cit @t  t ($t Nt .n$.t NrV2t N bt :x$xt Z6t V5$5t Ot9t  [t }Kt }Kt Jr2t lt 6Vt <"<t t t I"It Dt V#t \it .t "t H|P!.t :#t pxBt $Jt t p@vt |~t 9"9t !t ^t t Bt Pt jt <#<t Jt #t $t j.0t 4|t t #t X t  t ht t ,0"0t ht \t kv"kt C et t ,A"At tt t dDd#Rt Pt \t :n"nt t  Yt #t vG!it t lt @CrWt f}/t W#Wt ht \t( fr#(t) (~t*  t+ #t- ~L"t,  # t. d2t/ t0 zt3 pt1 zt4 t2 zt7 ~" t8 B bt9 8"8t; l*t: zt< l*t= t> z8t? lpt@ Hw"wtA tB h~tC tD "tF , # tG , # tR p >" tQ  tP  ! tO D * tN  tM Z j tJ  Z"8 tV ^ tW ($@ tT \ tU @*""tS "8tY bjTtZ v(t[ "t] V $tp 1#_ tq *ntr (ts <#<tu ~l!Ltt P FfLtv #t v %t t ,t #t 6h"t tt $#$t #Ft $t "8t ,1#1t t f$ t Vt !t 4($4t y#yt j#` t Qn$ t $t t     VX[]8:egkn~eh0257eg#%&)(+nq} !!!!""""""""""""######!$%$%%'%*%J%L%O%R%h%j%~%%%%%%%%%&)&6&8&I&K&N&Q&T&V&h&k&&&&&&&&'c'i'Y(\((((((( ))5)9)))))))******F*H*o+r+++++,,-------- ......+...e.i.}......//////11 3"3%3'3J3L3[3^3l4o4{4~4444444667777t7v777783858888899999999: :::;;;;x;z;;; < <A<C<<<<<9>;>X>Z>]>`>p>s>>>>>>>>>>>@@(@+@8@<@J@M@a@d@@@FFFFGG5H7HIIIIIIIIyJ|JJJJJJJLLLMOO>O@OjOlOOOOOMPOPSPUPWPYPQQQQR!RFRHRKRMRRRSS=T?ToTqTtTvTTT[V^VVVVVZ"Z1Z3ZrZvZZZZZ\\\\\\] ]]!]2]5]T]W]Z]]]]]]]]]]]^^8^:^I^^^____U`W`c`e`aTippensaulaul Normal.dotpPaul E. Tippens93lMicrosoft Word 8.0@kx@,L @hG@\ M ՜.+,D՜.+,8 hp  SPSU 'y_1 DocumentSummaryInformation8CompObjj Chapter 2 Title 6> _PID_GUIDAN{3ECA96CA-F670-11D2-B9D0-44455354616F}  FMicrosoft Word Document MSWordDocWord.Document.89q2GLM 5Ti5 J   Lgln1Rgh}Vk :OPe g$h$%%}&&''(((())))))]*^*(-*-@.U.....61?1L1M12)2=2R2j2k233P5Q55 6&6;6M6N688L:M:<<====>>@@@@@AUCWC>D@DcEeEG:G=GCGZGwG}GGH/HIHKHIIeJgJKKLLLLLMMMyPzPPPRRTTTTZUZUVVVVJYJYLYNYTZiZZZZZ[[[[![#[\\\\R\R\_\t\\\]]]F^H^I^I^Q^R^T^i^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^__________________ _ _ _ _ _ _ _ _ _ _____________________________________ _ _!_!_"_"_#_#_$_$_%_%_&_&_'_'_(_(_)_)_*_*_+_+_,_,_-_-_._._/_/_0_0_1_1_2_2_3_3_4_4_5_5_6_6_7_7_8_8_9_9_:_:_;_;_<_<_=_=_>_>_?_?_@_@_A_A_B_B_C_C_D_D_E_E_F_F_G_G_H_H_I_I_J_J_K_K_L_L_M_M_N_N_O_O_P_P_Q_Q_R_R_S_S_T_T_U_U_V_V_W_W_X_X_Y_Y_Z_Z_[_[_\_\_]_]_^_^_____`_`_a_a_b_b_c_c_d_d_e_e_f_f_g_g_h_h_i_i_j_j_k_k_l_l_m_m_n_n_o_o_p_p_q_q_r_r_s_s_t_t_u_u_v_v_w_w_x_x_y_y_z_z_{_{_|_|_}_}_~_~______________________________________``` ` ` `````#`$`/`0`6`7`D`E`Q`R`T`U`b`c`p`q`z`{``````````````````````````` a aaaaaaaaaaa a!a$a%a'a(a*a+a-a.a0a1a4a5a8a9aHaIaWaXaZa[aeafa~aaPaul E. Tippens"C:\Word Files\Answers\ANSCHAP6.docPaul E. Tippens"C:\Word Files\Answers\ANSCHAP6.docPaul E. Tippens"C:\Word Files\Answers\ANSCHAP6.docPaul E. Tippens"C:\Word Files\Answers\ANSCHAP6.docPaul E. Tippens"C:\Word Files\Answers\ANSCHAP6.docPaul E. Tippens"C:\Word Files\Answers\ANSCHAP6.docPaul E. Tippens1C:\windows\TEMP\AutoRecovery save of ANSCHAP6.asdPaul E. Tippens"C:\Word Files\Answers\ANSCHAP6.docPaul E. Tippens"C:\Word Files\Answers\ANSCHAP6.docPaul E. Tippens1C:\windows\TEMP\AutoRecovery save of ANSCHAP6.asd@>]>]P{  >]>]ap@G:Times New Roman5Symbol3& :Arial"qht*5f\AF=5]^ M'"0dy_ Chapter 2Paul E. TippensPaul E. Tippens