Find a formula, using the cosine function, for your height above ground after t minutes on the ferris wheel.

Question

A ferris wheel is 6 meters in diameter and boarded in the six o'clock position from a platform that is 6 meters above the ground. The wheel completes one full revolution every 6 minutes. At the initial time t equals 0 you are in the twelve o'clock position.


Find a formula, using the cosine function, for your height above ground after t minutes on the ferris wheel.

Answer 1

The formula is:

 

Height = 3 cos(pi*t/3) + 9

 

The center of the ferris wheel is 9 m above the ground, so that is how high up it is displaced and accounts for the "+ 9" term

 

The ferris wheel has an amplitude of 3, causing it to vary from 9-3=6 m to 9+3=12 m above the ground.

 

The ferris wheel has a period of 6 minutes, so its angular rate is (2pi radians)/(6 minutes) = pi/3.  Multiply that by time to get the angle (pi*t/3).

 

Click on the link below for a graph of the problem:

 

http://www.wyzant.com/resources/files/286001/ferris_wheel_problem