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Posted by **terry** on Wednesday, December 5, 2012 at 1:14am.

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 -
**Steve**, Wednesday, December 5, 2012 at 11:50amIf 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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