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 center of the Ferris wheel as a function of time.

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

Answer 1

1. See attached picture:

2. Radius of the Ferris wheel is 60/2 = 30 feet.

The center of the Ferris wheel is 30 +2 = 32 feet.

At the bottom you are 2 feet off the ground at 0 seconds.

At 30 seconds you are in line with the center of the Ferris wheel (32 feet).

At 60 seconds (1 minute) you are at the top ( 62 feet ).

At 90 seconds you are in line with the center of the Ferris wheel (32 feet).

At 120 seconds ( 2 minutes) you are back at the bottom (2 feet).

This is a cosine function written as y = Acos(Bx) +C

where A is the amplitude ( the difference between the center and the top written as a negative, which in this case is the radius of the Ferris wheel as a negative.

A = -30

B is found using the period formula 2PI/B , period is the time so you have:

120 = 2PI/B

Multiply both sides by B:

120B = 2PI

Divide both sides by 120:

B = 2PI/120

Simplify:

B = PI/60

C is the center point of the Ferris wheel, which is 32.

The function becomes: Y= -30cos(PIx/60)+32

Now to write as a function of time, replace y with H9t) and x with t:

h(t) = -30cosPIt/60)+32