A particle strikes a smooth inclined plane horizontally and bounces back in the vertically upward direction. If the incline makes an angle of 60 deg with the horizontal, find the coefficient of restitution between the particle and the inclined surface.

1/3
1/sqrt(3)
1/2
1

Correct answer: 1/3

Solution

Setting the x-component of the rebound velocity to zero gives cos²(60 deg) = e * sin²(60 deg), so e = cos²(60 deg)/sin²(60 deg) = (1/4)/(3/4) = 1/3.

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