At the state fair, the giant Ferris wheel takes 48 seconds to make one full rotation. The Ferris wheel has a diameter of 60 ft. and the bottom of the wheel is 8 ft. above the ground. If you are the last person on the Ferris wheel and you board at the bottom, which equation below models your height above the ground as a function of time?

Answer: H = 30ft*cos (2*pi*t/48s + pi) + 38ft.

Step-by-step explanation:

We can use a trigonometric function to model this, let's use:

H = A*cos (w*t) +

where A is a constant, w is the frequency, t is time, and h is of the wheel, this is half the diameter plus the distance above the ground:

30ft + 8ft = 38ft.

A is equal to the radius of the wheel, or half the diameter, A = 60ft/2 = 30ft.

we know that the period is 48 seconds, this means that:

cos (w*0) = cos (w*48s) = 1

then w*48s = 2*pi

w = 2*pi/48s

so now function is:

H = 30ft*cos (2*pi*t/48s) + 38ft.

But we also know that, at t = 0, you must be at the bottom of the wheel, so we must ad a phase of pi to the cosine function

H = 30ft*cos (2*pi*t/48s + pi) + 38ft.

So now when t = 0, we have:

H (0) = 30ft*cos (0 + pi) + 38ft. = 8ft.