I can do the Ferris Wheel type. This one I can not solve.
A light is attached to a 13 inch radius bicycle tire, at a point 8 inches from the center. If Harvey rides the bike at 15 mph, how fast is the light moving up and down at its fastest?
If I've done my conversion properly
15 mi/hr = (15*5280*12)/(13*3600) = 264/13 rad/s
so, the height of the point is
y = 8sin(2pi/(264/13) t)
so, when is the velocity fastest?
v = y', so v is max where y''=0.