Question

A Ferris wheel of diameter 18.5m rotated at a rate of 0.2rad/s. If passengers board the lowest car at the height of 3 m above the ground, determine a sine function that models the height, h, in metres, the car relative to the group as a function of the time, t, in seconds

Answer 1

radius = 9.25

how long to go 2 pi radians?
.3rad/sec * T = 2 * 3.14
T = 20.9 seconds for a revolution
height = 3 + 9.25 at center = 12.25
so if it is at the low point at t = 0
h = 12.25 + 9.25 sin (2 pi t/T - pi/2)
the pi/4 is to make it sin (-pi/2) = -1 at t = 0 so it is at 3 m at t = 0

Answer 2

Typo
the pi/2 is to make it sin (-pi/2) = -1 at t = 0 so it is at 3 m at t = 0