Help with theses answers plz

Question

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

1)Create a graph that represents your height relative to the center of the Ferris wheel as a function of time,using the image below as a guide.

2)Create a function that represents your height relative to the center of the Ferris wheel as a function of time.

Answer 1

The cosine function starts at the top and goes down and back up, just like this situation so the easiest choice is to use a cosine function. We want the period to be 2 minutes (the time it takes to make one cycle). So the graph would look like this:

The function would have an amplitude of 30 because you go up and down 30 from the neutral position. Since the Ferris wheel is 2 feet off the ground, the neutral position is at 32 feet. So the vertical shift is 32.

Since the period is 2, to find out what number we put in front of the time variable ("t") as the horizontal stretch/compression factor, we take the normal cosine period (2π) and divide by the period (2). So the multiplier is 2π/2 = π. That makes the function:

H(t) = 30cos(πt) + 32 where H is height in feet and t is time in minutes