# Calc-math

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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?

• Calc-math -

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.

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