Question

A ferris wheel with a 40-ft diameter rotates once every 30 seconds. the bottom of the wheel is located 1.5 feet above the ground. you get on at the very bottom of the ferris wheel at time t = 0 and then the ferris wheel begins to turn counter-clockwise. for the problems below, assume the wheel makes 2 full rotations.

a. at what times are you at the top of the ferris wheel? what is the height at the top of the ferris wheel?


b. at what times are you at the bottom of the ferris wheel? what is the height at the bottom of the ferris wheel?


c. at what times are you in the exact middle of the ferris wheel? what is the height of the exact middle of the ferris wheel?


d. write a cosine function to model your height above the ground over time, t.

Answer 1

Explanation:

Let y = -A cos B(t -c) + D

A, amplitude = 20ft

Period = 2π / B ( B = π / 15)

= 30

c = 0

Vertical shift D = 21.5 ft

Equation becomes

`y= -20 \cos (\pi)/(15)( t-0)+21.5`

`\to y=-20\cos (\pi)/(15) t+21.5`

a) Top of the ferris wheel is

t = 15sec, 45sec, height = 41.5ft

b) At the bottom of the ferris wheel

t = 0, 30sec, 60 sec

height = 1.5ft

c) Exact middle of the ferris wheel

t = 15/ 2 = 7.5sec, 22.5sec, 37.5sec, 52.5sec

d)
`f(t) or h = -20 \cos ((\pi)/(15) t)+21.5`