Answer These Six Questions

Question

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.

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

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 .

If the ferries makes one rotation in 2 minutes, then at t=0 the passenger's height at the top is 62 feet, and after 1 minute, the passenger's height is 32 feet, finally at t = 2 the passenger's height is 62 feet again.

To graph, you need a t-chart as follow

t = 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 5.5 6

H = 62 32 2 32 62 32 2 32 62 32 2 32 62

So you can sketch its graph like an alternative function.

2.

if the passenger on the ferries rotates 2 pi (a whole circle) in 2 minutes starting from the top, then it rotates a pi after 1 minute and pi . t after t minutes and therefore drawing a right triangle with the central angle (pi . t) and using its cosine, the passenger's height will be 30 Cos (pi t) from the center and 30 Cos(pi t) + 32 from the ground. So: H = 30 Cos(pi t) + 32. H is the height of the passenger from the ground.

4.

Plugging t = 8.5, will result: H = 30 Cos(8.5 pi) + 32 = 30 Cos (8 pi + pi/2) +32 = 30 Cos (pi/2) +32 = 0 + 32 = 32

5.

The T-Chart will be

t = 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 5.5 6

H = 32 2 32 62 32 2 32 62 32 2 32 62 2

6.

The function will be shifted 8.5 minutes to the left. So the new function will be:

H = 30 Cos( pi(t+17/2)) +32 which is the same function as:

H = 30 Cos (pi(t + 8 + 1/2)) +32. Since Cos (8pi + a) = Cos a therefore:

H = 30 Cos (pi(t + 1/2)) + 32.