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Question

Continued from the previous practical assessment. A Ferris wheel has a diameter of 60 feet. When you start at the top of the Ferris wheel, you are 62 feet from the ground. The Ferris wheel completes one rotation in 2 minutes.

1. Create a graph that represents your height relative to the ground as a function of time, using the image below as a guide. Replace the image with your graph.

2. Now create a function that represents your height from the ground as a function of time.

3. Compare the function from the previous practical and the one above. Explain what the two functions have in common and what is different. Specifically mention the amplitude, period, and any transformations

to map the first function to the second.

4. If the Ferris wheel stops after 8.5 minutes, how high from the ground would you be? Use the appropriate function from above.

5. The Ferris wheel starts again from the position you had in question 4, resetting to time = 0. Create a graph that represents your height relative to the ground as a function of time, using the image below as a guide. Replace the image with your graph.

6. Create a new function of the height from the ground as a function of time for the situation in question 5.

Answer 1

1) We have:

d=60, so r=30

h₀=d+2=62

rotation speed ω=180^o/minute

so the h(t)=h₀-x(t), where x(t) is the difference between h_o and the current t high h(t)

x(t)=R-R*cosθ(t), where θ(t) is the angle between the initial (top) possession and the current t position.

θ(t)=ω*t=180^o*t

so h(t)=62-(30-30*cos(t/2))

h(t)=32+30*cos(180^o*t)

to build the graph you need to go through points t=0, 1/2, 1, 3/2, 2 and then repeat

h(0)=62

h(1/2)=32

h(1)=2

h(3/2)=32

h(2)=62

so the graph will be a sinusoid starts from point (0,2) with A=30 and middle high=32, and period = 2 minutes

I can't add a picture

2) h(t)=32+30*cos(180^o*t)

3) I don't see the previous pratical

4) 8.5 minutes = 4 periods + 1/2 minute, so the h(8.5)=h(1/2)=32

5) h(t)=32-30*sin(180^o*t)

so the graph will be a sinusoid starts from point (0,32) with A=30 and middle high=32, and period = 2 minutes

6) h(t)=32-30*sin(180^o*t)