Question

A ferris wheel has a radius of 13 m. It rotates once every 24 seconds. A passenger gets on at the bottom
of the wheel from a ramp which is one metre above ground level.

a) If the height of the passenger is measured from the ground, determine an equation for the height of the
passenger as a function of time in the form of h(t)= acos(bt)+d
b) To the nearest metre, find the height of the passenger after 55 seconds.

Answer 1

since cos(t) has a max at t=0, and we want the passenger to start at the bottom, a will be negative.

r=13, so

h(t) = -13cos(bt)+d

h(0) = 1, so

h(t) = -13cos(bt)+14

The period is 24, so

h(t) = -13cos(π/12 t)+14