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 classmatesÃ¢â‚¬â„¢ 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 Ã¢â‚¬â€œ 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

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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 oÃ¢â‚¬â„¢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 personÃ¢â‚¬â„¢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.