Pre-Calculus sem 2, 2011 gift 4: Ferris Wheel Story



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Pre-Calculus SEM 2, 2011


GIFT 4: Ferris Wheel Story
The 1893 Chicago World’s Fair is considered the birthplace of the classic amusement park ride, the Ferris wheel. The architectural wonder was created by an American engineer named George Ferris. The original Ferris wheel no longer exists. But, in 1990, a new Ferris wheel was built at Navy Pier in Chicago to resemble the original. While the Navy Pier Ferris Wheel is a beautiful Chicago landmark, its grandeur actually pales in comparison to Mr. Ferris’ creation.
The Ferris wheel built for the World’s Fair had a diameter of 250 feet. It stood 14 feet off the ground. It had 36 wooden boxcars that were the size of train cars. Each car could hold 60 people! The wheel would load cars in such a way that each rider could enjoy a full rotation that lasted about 10 minutes.
The Ferris wheel at Navy Pier has a diameter of 140 feet. It stands 10 feet off the ground. The wheel has 40 gondolas that seat six passengers each. It takes about 6 minutes for the Navy Pier Ferris Wheel to complete one rotation.
Below is a picture of the first Ferris wheel next to the Ferris wheel at Navy Pier.



GIFT 4: Ferris Wheel Comparison Pre-Calculus

GIFT DESCRIPTION and GUIDELINES:

Purpose:

In real life, ferris wheel ride is one of the best and most common examples of periodic change and circular functions. In this project, you will apply your knowledge of trigonometric functions acquired in Unit 4 to analyze, write equations for, and model a ferris wheel ride graphically. You and your partner will compare trigonometric functions that model the original World’s Fair Ferris Wheel and Navy Pier Ferris Wheel and find values of these trigonometric functions.

Materials to be turned in:

Report that demonstrates your complete work process and final answers to all parts of the project. You are provided a template for your report, some parts are pre-typed for you and some require your own work to fully answer the prompt. You have a choice of :



  1. typing your responses directly into the template provided or

  2. printing a hard copy and neatly handwriting your responses into the template of the document

Your final report (typed or handwritten) must be on a white copy paper, NOT a notebook paper. Make sure you read prompt carefully and answer ALL parts of the problem. Show all necessary work to support your answers in your report! Clearly identify your final answer(s) in a sentence form!


IMPORTANT NOTE: Graphs of the functions are to be inserted ELECTRONICALLY INTO THE DOCUMENT before printing it! If you require assistance with creating and/ or inserting of the graphs into your report, do not wait till the last minute!
Project Evaluation Criteria:

Your report will be assessed based on accuracy of all questions you are required to answer in your report. Make sure you clearly mark your answers and that you justify your answers where required. Show any necessary work to support your answers.

Professional appearance of your report is equally as important as the work. Please, make sure to create a TITLE PAGE for your report. Report template that follows does not include the cover page.

You may consider inserting header/footer to label each page of your project, page numbers, etc.

Your complete report should be approximately 4 pages (including cover)


World’s Fair Ferris Wheel and the boarding platform.

1] List given info:
2] Let h represent your vertical position (height) at time t where t is given in minutes.

Identify 5 critical t-axis values.


t

h


d =



















h =














3] Ride procedure:
4] Characteristics of the periodic function:


  1. Phase shift b) Vertical shift c) Amplitude d) Period e) y-intercept

f) Min. value g) Max. value h) t(0)

5] Write one cosine and one sine rule to model your curve.

(Remember, there are multiple possible answers!!)


6] Provide a graph of your equation. (Electronic version of the graph must be inserted here! Your graph MUST include values on the x-axis and the y-axis.)
7] Answer the following questions. SHOW ALL WORK!


  1. What is the circumference of the wheel?


  1. At what speed is the wheel traveling? Please give your answer in feet/second.




  1. If you begin your ride at the base of the wheel, what is your height after

1 minute? 4 minutes?

  1. At what approximate time(s) will you reach the following heights?

100 ft. 240 ft.



Navy Pier Ferris Wheel and the boarding platform.

1] List given info:
2] Let h represent your vertical position (height) at time t where t is given in minutes.

Identify 5 critical t-axis values.

t


h


d =



















h =














3] Ride procedure:
4] Characteristics of the periodic function:


  1. Phase shift b) Vertical shift c) Amplitude d) Period e) y-intercept

f) Min. value g) Max. value h) t(0)


5] Write one cosine and one sine rule to model your curve.

(Remember, there are multiple possible answers!!)


6] Provide a graph of your equation. (Electronic version of the graph must be inserted here! Your graph MUST include values on the x-axis and the y-axis.)
7] Answer the following questions. SHOW ALL WORK!


  1. What is the circumference of the wheel?


  1. At what speed is the wheel traveling? Please give your answer in feet/second.



  1. If you begin your ride at the base of the wheel, what is your height after


1 minute? 4 minutes?

  1. At what approximate time(s) will you reach the following heights?

100 ft. 240 ft.



Ferris Wheel Comparison Challenge


I) Imagine the Navy Pier and the World’s Fair Ferris Wheel being built beside each other. If both wheels begin turning at once, over a 20 minute time period, at what times are the wheels at the same height?

SHOW ALL WORK and PROVIDE A GRAPH.

II) What is the length of the arc traveled by the Navy Pier Ferris wheel from the


4 o’clock to the 7 o’clock position? SHOW ALL WORK !




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