Answer These Two 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. 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. Replace the image with your graph.
2. 
3. 2. Create a function that represents your height relative to the center of the Ferris wheel as a function of time.

Answer 1

f(t) = AsinB(t-C) +D

D = midline = 0

A = Amplitude = 30

B = 2pi/period =2pi/2 = pi

C = phase shift =0

f(t) = 30sinpi(t-C) +32

at t=0, f(0) =30sinpi(0-C)=0

sinpi(-C) = 0

pi(-C) = 0

-C = 0

C =0

f(t) = 30sinpi(t)

it has a standard sine wave graph, but stretched vertically by a factor of 30

and the period shortened from 2pi to 2, or compressed horizontally by a factor of 1/pi