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Question

A ball is projected form a point A on a smooth inclined plane which makes an angle α to the horizontal. The velocity of projection makes an angle θ with the plane upwards. If on the second bounce the ball is moving perpendicular to the plane, find e in terms of α and θ. Here e is the coefficient of restitution between the ball and the plane

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Solution

FirstbouncewillbeatthetimeT1=2usinθgcosαSecondbouncewillbeatthetimeafterthefirstbounceT2=2eusinθgcosαsincevelocityalongvdirectionafterthe1stbounceiseusinθ.IntimeT1+T2thevelocityalongxdirectionbecomeszerothus,0=ucosθgsinα(T1+T2)0=ucosθgsinα2usinθgcosα(1+e)e=cotθcotα21

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