# Ferris Wheel Is 29 Meters in Diameter Discussion

### Description

Mathematical models are constructed for many different practical applications, and we start to build some of them in this course. This discussion begins with a simple geometric model.

For your initial post, you must do the following:

- Solve the problem in the Mobius module discussion.
- Explain how you got your results in the Brightspace module discussion.

For your response posts, you must do the following:

- Comment on your classmates’ analyses and their answers. Compare and contrast your problem-solving approach to how your classmates solved the problem.
- Review the explanations given by your peers for their problem-solving strategies. Your comments may focus on the following:
- How did they describe steps to make their explanations clear?
- What additional details could they have included?
- What details did they include that you may not have?
- What changes would you make to your initial post?

- Reply to at least two different classmates outside of your own initial post thread.

## 6-1 Trigonometric Models

Contains unread posts

Michael Foisy posted Apr 7, 2021 12:17 PM

A Ferris wheel is 27 meters in diameter and completes 1 full revolution in 16 minutes

A:.

- Amplitude: A = 13.5

27/ 2 – which is half the height of the Ferris wheel.

Midline: h = 14.5

13.5 + 1 = 14.5 – half the height of Ferris wheel +1 for the platform being 1 meter above ground.

Period: P = 16

1 full revolution every 16 minutes

B:

- h = -Acos(B*t)+C

h(t) = -13.5cos(Pi/8*t)+14.5

C:

- If the Ferris wheel continues to turn, how high off the ground is a person after 36 minutes? 14.5

Daniel Fiedorowicz posted Apr 6, 2021 7:43 PM

to Group 1

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Hello All,

A Ferris wheel is 22 meters in diameter and completes 1 full revolution in 16 minutes.

A. A Ferris wheel is 22 meters in diameter and boarded from a platform that is 1 meter above the ground. The six o’clock position on the Ferris wheel is level with the loading platform. The wheel completes 1 full revolution in 16 minutes. The function h(t) gives a person’s height in meters above the ground t minutes after the wheel begins to turn.

Amplitude: Based on the given information the Diameter of the Ferris wheel is 22 meters. The radius of the wheel is Diameter/2 so for this wheel the radius is 11 meters. Therefore the height will oscillate with amplitude of 11 meters above and below the center.

A= 11 meters

Midline: Passengers will get on the wheel 1 m above the ground, so the center of the wheel must be located 11+1=12 meters above ground level. The midline of the oscillation will be at 12 meters.

h= 12 meters

Period: The Ferris wheel takes 16 minutes to *complete* 1 revolution, so the height will oscillate with a period of 16 minutes. A person riding the wheel will board at the lowest *point* of the wheel and go up, making the function of the wheel a cosine function.

P= 16 Minutes

Shape= -cos

B. The basic Sinusoidal cosine function would be:

y=Acos(Bx?C)+D

In order to use this formula we need to calculate the value of the period:

2?|B|= 2?|16|=?8

so with that we can plug in the rest given information into the formula:

A=-11

B= ?8

C= 0

D= 12

x= time: t

h(t)=?11cos(?8t)+12

C. If the Ferris wheel continues to turn, how high off the ground is a person after 60 minutes?

I inserted 60 into our function as the value for t, then used excel to find the correct answer.

h(60)=?11cos(?8(60))+12=12

After 60 minutes of riding the wheel the person is 12 meters off the ground.

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