Q:

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

Accepted Solution

A:
1. See attached picture:2. Radius of the Ferris wheel is 60/2 Β = 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) +Cwhere 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 = -30B is found using the period formula 2PI/B , period is the time so you have:120 = 2PI/BMultiply both sides by B:120B = 2PIDivide both sides by 120:B = 2PI/120Simplify:B = PI/60C is the center point of the Ferris wheel, which is 32.The function becomes: Y= -30cos(PIx/60)+32Now to write as a function of time, replace y with H9t) and x with t:h(t) = -30cosPIt/60)+32