While watching TV, you see a circus show in which a performer drives a motorcycl

Question

While watching TV, you see a circus show in which a performer drives a motorcycle around the inside of a vertical ring of radius R. You wonder how far from the base of the ring the cycle would fall if the rider made a mistake at the top of the loop and fell off the track so you decide to calculate it. You determine that the cycle is going around at a constant speed v and that it takes at most 4.0 seconds to get around the ring. At this speed, the motorcycle just barely loses contact with the ring at the top when it is upside down and is in free fall.

Explanation / Answer

speed for barely falling at the top = (Rg)^(0.5)

time taken to fall vertically = (2*(2R)*/g)^(0.5)

distance traversed in this much time with the speed above = [ (Rg)^(0.5)]* (2*(2R)*/g)^(0.5) = 2R

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