Write an equation about the movement of a Ferris wheel.

Question

A Ferris whee with a radius of 15m rotates once every 100 seconds. Riders board the Ferris wheel using a platform that is 1 m above the ground.

1, draw the graph for two rotations of the Ferris wheel.

2, write a function that gives the height of the rider as a function of time.

3, in one rotation, how many seconds is the rider higher than 16m ?

Answer 1

h(t) = a·cos(b(t-c)) + d

1. a = amplitude = -15. It's negative so you start at the bottom of the cycle rather than the top
2. b = frequency = 2π/period = 2π/100 = π/50
3. c = phase shift = 0
4. d = vertical shift = location of midline = 15 m + 1 m = 16 m

h(t) = -15·cos(π·t/50) + 16

The midline is at 16 m, so you spend half of the time above 16 m and half below. One rotation takes 100 seconds, so you spend 50 seconds above 16 m every rotation.