ࡱ> &(%[ B'bjbj 48ΐΐBNN,O^KKKK~~~$~~~~KK    ~.KK ~   KI2 0O 5 5 5  ~~ ~~~~~~~~O~~~~5 ~~~~~~~~~N W:  Pre-Calculus Internet Project - Tidal Waves and Sine Curves Focus The focus of this project is to give you an opportunity to find and analyze real-world data from the internet regarding high and low OCEAN tides anywhere in the world and then to find the equation of a sine function that models that behavior. Objectives * Collect and organize the real-world data * Present this data on a T-chart and then on a Cartesian Coordinate Plane * Analyze and interpret the data * Calculate a function to model the data and make a prediction Overview . The tide is caused by the pull of the sun and the moon on the oceans and the rotation of the earth, but its exact pattern at any particular location on the coast depends very strongly on the shape of the coastline and on the profile of the sea floor nearby. Even though the forces that move the tide are completely understood, the tides at any given location are essentially impossible to calculate theoretically. What we can do is to record the height of the tide at that location over a certain period of time, and use these measurements to predict the tides in the future. Directions: 1. Your link on the Web is:  HYPERLINK "http://tbone.biol.sc.edu/tide/sitesel.html" http://tbone.biol.sc.edu/tide/sitesel.html 2. Select a region from this page and then choose a site from the next page. Do NOT choose a site that ends in current. Do NOT choose a basin, bay or river.  3. Scroll down and select the prompt Make a Prediction Using Options 4. Set the following two options: Change Select Presentation Options to 3 days Change Starting Time and Time Display Options to start sometime between April 1 and August 15, 2009 at 0:00.  5. Click on Make Prediction Using Options 6. Print out the data (just the first page) that shows the dates, times and tidal heights. You will include this print-out in your project. Be sure that you have 2 high tides and 2 low tides for ALL THREE days. Pick a location where the tides are at least 3 feet or meters in difference. 7. Using the data from your print-out, convert all times (hours and minutes) into decimal hours by dividing the minutes by 60 and round to 2 decimal places. Ex. 2:15 = 2.25 8. Find the equation of the sine curve that best fits this data by following the directions on the subsequent data page. 9. Put your information into a T-chart, using time for the independent variable (x-axis) and tide height for the dependent variable (y-axis). Your project begins at time 0.00 on Day 1 and ends with time 72.00 on Day 3. You need to add 24 hours to all your times on Day 2 and 48 hours to all your times on Day 3 before you graph, so that your x-values run from 1 -72. 10. Using graph paper or the computer, plot the data from your T-chart, connecting the points with a smooth curve (not segments) and scaling the axes according to your needs. The two axes may be scaled differently. You will have two graphs on one set of axes one from the raw data and the second from your sine equation. Be sure to state the sine equation with your graph. Presentation: Your final project is due on March 30th. You may turn your project in early and late projects will lose 10% for each day late. Your project must be typed, double-spaced and must include, in this order *A cover page that includes: The name of the project Your name Pre-Calculus Class period Date Due Teachers name * Page 1: An introduction to the project, including the location you chose, the length of time and dates selected and why you chose this particular place and time of year. * Page 2: The print-out of the data from the Internet * Page 3: The data page, including the T-chart with your original data. Make sure your mathematical calculations are correct! * Page 4: The graphs of the data and your sine equation on one set of axes. State the sine equation. * Page 5: A summary of the project answering these questions 1) State any tendencies that you saw in the high and low tides. For example, were there any consistencies between the time or height of the high/low tides from day to day. 2) Is there a predictable pattern? 3) Might the moon have had an influence on this pattern? (your print-out might have information about this) 4) State at least one other natural phenomena that is also predictable by means of a periodic sine wave or curve. 5) Predict the height of the tidal wave at 11am on the 6th day. FINDING THE EQUATION OF YOUR SINUSOID Analysis: Follow the directions below for finding a sine equation that best fits your data. Your equation will be in the general form y = a sin (bx-h) + d. Throughout this page, round your decimals to three places. a) Find a, the amplitude. The amplitude is one-half the difference of your largest and smallest y-coordinates. (Hint-you may need to make a negative. Look at your data and decide.) Enter your value for a here: _____________________ b) Find b, the value that determines the period of the function in these two steps. First find the new period: P = the difference of the x-coordinates of 2 consecutive high tides. EMBED Equation.3  Enter your value for P here: __________________ Second, the new period  EMBED Equation.3  , therefore  EMBED Equation.3 . Enter your value of b here: ___________________ c) Find d, the vertical shift. The vertical shift is the average of the largest and smallest y-values. Enter your d value here:______________ d) Find h, the horizontal shift. Let t equal the time of your first high tide and use the following formula to find the value of h:  EMBED Equation.3  Enter your value of h here: __________________ e) Put it all together and write the equation of the sine curve in the form from y = a sin (bx-h) + d. Enter your equation here: _______________________________________ Create a T-chart like the one shown below and include it with your project. The y-values for your sine equation can be found using you graphing calculator. Enter your equation under y=. Remember, to get the coordinates for your equation, set your Table Set to Indpnt: Ask. Use the table to plug in the x-values that you have under time to find the corresponding y-values.  TIME (x-values) RAW DATA (y-values) SINE EQUATION (y-values) Domain: 0-72 hrs high/low tide heights using your calculator  Name: Tidal Wave Project Rubric 50 Point Project Presentation (0-10 points) a. cover page with required information _______(2 pts) b. stapled or bound in some manner before class _______(2 pts) c. typed clearly, neatly, and double-spaced _______(2 pts) d. graphics/charts are clearly labeled and easy to understand; appearance is neat _______(2 pts) e. followed directions throughout the project _______(2 pts) Computations: (0-20 points) a. times are correctly converted _______(5 pts) b. T-chart/sine values are correct on data page _______(5 pts) c. equation of sine curve has been computed correctly _______(5 pts) d. raw data and sine curve are correctly displayed on one set of axes _______(5 pts) Written Explanation: (0-20 points) a. grammar and spelling are correct _______(2 pts) b. math words are appropriately used _______(2 pts) c. explanations are easy to follow and understand _______(4 pts) d. introduction _______(4 pts) e. conclusion where all questions are answered _______(6 pts) e. correctly predicted high tide at 11am on the 6th day _______(2 pts) Total points earned: ______/ 50 =>C: E # , u   NPW}~ 3456߰߰ߩߣߜߕ߈|j9hCJEHUjvK hCJUV h5CJ hCJH* hK3CJ h6CJjhCJUmHnHuh0JCJjhCJUjhCJU hCJ h>*CJhhOJQJh\'CJaJ,=>F9 : E r " # , s t u   z  -^gd$a$gd$a$gdN)^#$[\t_"#Ogd ]8qVW}~Z[`$a$gdgd`a7wxs: ; !!"z"}"""""""$a$gdgdCJ56IJKL!!"z"{"}"~"""""³Ѭѝ~w~ng_WR h5hOJQJhLOh5 hLOhh5OJQJ h6CJjhCJUmHnHujmhnohCJEHUjAL hCJUVaJ h>*CJjhnohCJEHUjAL hCJUVaJ hCJjhCJUjhnohCJEHUjAL hCJUVaJ"""""&&''?'@'A'B'ž h-`h-`h-` hLOhhhH*h h>*h5OJQJhLOh5CJaJh5CJaJ ""#U###=$>$Z$$$!%y%z%{%%%&\&&&'''@'B'gddhgd21h:pN)/ =!"#$`% 9DyK +http://tbone.biol.sc.edu/tide/sitesel.htmlyK nhttp://tbone.biol.sc.edu/tide/sitesel.htmlyX;H,]ą'cyDd T\  c $A? ?#" `24yS }7`!4yS   ȽXJkxcdd``d!0 ĜL0##0KQ* Wä2AA?H1Zc@øjx|K2B* R\``0I3^Dd \  c $A? ?#" `2RZ|F#B7`!RZ|F#B~`:PxڍQMK@}AD4zū"?V"L[H1ٓ(R=ҟ#(ŋowcAm[fMR|aq DZBb>ytd\YFk3X@,ɰ0*F<-E ha_H+a26&fm2;uy^ݯ;n8EYG.g5\ʜtPr=TV"݃!h?F~~,gϛQ?숼!}|sۥξ:u\ %^йlRTqg٘P][_Q|t/XK%Wo0 SEye]Dd \  c $A? ?#" `2a~pZbT7`!a~pZb~`:OxڍQJ@}Ɗ !z'E1SXhB %7z'xPA/Rƀڂ ơ d$*7"!$(cr6rtlyFXA,ɰ1z*CUv 0ǯo0B{/@\D)sS3*I(͎[nJSG{ 5h}Ia{PEm/ kX7W/IeN]CB綫0A=j~sjnK_KyA G"+ٔBϲQP_{Qp/XK%po0 LHus[Dd \  c $A? ?#" `2rQˎy0(57`!rQˎy0(5F@ MxuQMJ@Q HBu\^H Z(sTA}=KRܨ̤gތ@6l, "AIh%Vҽ܄b{6Dr?dtg+s)'mTidjeJx/ӝx(Va^ 'fuZ W7={S盞3JZ~Uqkf>ķ,oWG"TߐAPp9L.a{a)$'ٕNz~}]0.u7(t+q0y_-j  !"#$'*,+-./102D456789:;<=>?@ABCRoot Entry Fpo) Data WordDocument48ObjectPool 3@po_1266085063F3@EOle CompObjfObjInfo  !"#$%&') FMicrosoft Equation 3.0 DS Equation Equation.39q8hi  FMicrosoft Equation 3.0 DS Equation Equation.39qEquation Native #_1287143838 FEEOle CompObj fObjInfo Equation Native  B_1287143856FEEOle  2&` P=2b FMicrosoft Equation 3.0 DS Equation Equation.39q2&4 b=2PCompObj fObjInfoEquation Native B_1287143868FEE FMicrosoft Equation 3.0 DS Equation Equation.39q2:L h=t"t4Oh+'0Ole CompObjfObjInfoEquation Native V1Table35 SummaryInformation(DocumentSummaryInformation84CompObj(y $0 P \ h t Pre-Calculus Internet ProjectDouglas Griffin Normal.dotm 3Microsoft Office Word@@V>@Fiy@H՜.+,D՜.+,\ hp  Griffin Construction83 Pre-Calculus Internet Project Title 8@ _PID_HLINKSA)e+http://tbone.biol.sc.edu/tide/sitesel.html7^ 2 0@P`p2( 0@P`p 0@P`p 0@P`p 0@P`p 0@P`p 0@P`p8XV~_HmH nH sH tH @`@ NormalCJ_HaJmH sH tH DA`D Default Paragraph FontRiR  Table Normal4 l4a (k (No List 6U@6 U o Hyperlink >*B*phHH N Balloon TextCJOJQJ^JaJNN NBalloon Text CharCJOJQJ^JaJPK![Content_Types].xmlj0Eжr(΢Iw},-j4 wP-t#bΙ{UTU^hd}㨫)*1P' ^W0)T9<l#$yi};~@(Hu* Dנz/0ǰ $ X3aZ,D0j~3߶b~i>3\`?/[G\!-Rk.sԻ..a濭?PK!֧6 _rels/.relsj0 }Q%v/C/}(h"O = C?hv=Ʌ%[xp{۵_Pѣ<1H0ORBdJE4b$q_6LR7`0̞O,En7Lib/SeеPK!kytheme/theme/themeManager.xml M @}w7c(EbˮCAǠҟ7՛K Y, e.|,H,lxɴIsQ}#Ր ֵ+!,^$j=GW)E+& 8PK!Ptheme/theme/theme1.xmlYOo6w toc'vuر-MniP@I}úama[إ4:lЯGRX^6؊>$ !)O^rC$y@/yH*񄴽)޵߻UDb`}"qۋJחX^)I`nEp)liV[]1M<OP6r=zgbIguSebORD۫qu gZo~ٺlAplxpT0+[}`jzAV2Fi@qv֬5\|ʜ̭NleXdsjcs7f W+Ն7`g ȘJj|h(KD- dXiJ؇(x$( :;˹! I_TS 1?E??ZBΪmU/?~xY'y5g&΋/ɋ>GMGeD3Vq%'#q$8K)fw9:ĵ x}rxwr:\TZaG*y8IjbRc|XŻǿI u3KGnD1NIBs RuK>V.EL+M2#'fi ~V vl{u8zH *:(W☕ ~JTe\O*tHGHY}KNP*ݾ˦TѼ9/#A7qZ$*c?qUnwN%Oi4 =3ڗP 1Pm \\9Mؓ2aD];Yt\[x]}Wr|]g- eW )6-rCSj id DЇAΜIqbJ#x꺃 6k#ASh&ʌt(Q%p%m&]caSl=X\P1Mh9MVdDAaVB[݈fJíP|8 քAV^f Hn- "d>znNJ ة>b&2vKyϼD:,AGm\nziÙ.uχYC6OMf3or$5NHT[XF64T,ќM0E)`#5XY`פ;%1U٥m;R>QD DcpU'&LE/pm%]8firS4d 7y\`JnίI R3U~7+׸#m qBiDi*L69mY&iHE=(K&N!V.KeLDĕ{D vEꦚdeNƟe(MN9ߜR6&3(a/DUz<{ˊYȳV)9Z[4^n5!J?Q3eBoCM m<.vpIYfZY_p[=al-Y}Nc͙ŋ4vfavl'SA8|*u{-ߟ0%M07%<ҍPK! ѐ'theme/theme/_rels/themeManager.xml.relsM 0wooӺ&݈Э5 6?$Q ,.aic21h:qm@RN;d`o7gK(M&$R(.1r'JЊT8V"AȻHu}|$b{P8g/]QAsم(#L[PK-![Content_Types].xmlPK-!֧6 +_rels/.relsPK-!kytheme/theme/themeManager.xmlPK-!Ptheme/theme/theme1.xmlPK-! ѐ' theme/theme/_rels/themeManager.xml.relsPK] B 8"B'^`"B' 355IKBX::::8  @P (  VB  C D"?VB  C D"?VB  C D"?J"    #" `?J"    #" `?B S  ?zB t D9t tth%tDJDFPs}af  z |   e i ! W [ `dVZy YV_[d")&]mD3333333333333333333333333333333333333333333333@AD@D&%G}+\'N)z7+;1wJ7)N9OU-`U oupnr@Kwb~nP^NlIgX`0K3mA&5^&bbQNu= BD@99g99BX@UnknownG* Times New Roman5Symbol3. * ArialCNComic Sans MSMCentury Schoolbook5. *aTahomaA BCambria Math"qh=C& KԆ88!24d332qHP ?N)2!xxPre-Calculus Internet ProjectDouglas Griffin   F'Microsoft Office Word 97-2003 Document MSWordDocWord.Document.89q