Question

A truck tire has a diameter of 4 feet and is revolving at a rate of 45 rpm. at t = 0, a certain point is at height 0. what is the height of the point above the ground after 15 seconds?

Answer 1

45 rpm=2π rad*45/60=1.5π rad/sec
radius=1.5 ft
axle at 2 ft and up and down from there:
thus
y=2-1.5cos(1.5πt)
to make y=0 at 0
at 15 sec
y=2-1.5cos(15*1.5π)
y=2-0
y=2 ft