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A ball of mass m strikes the fixed incli...

A ball of mass m strikes the fixed inclined plane after falling through a height h. if it rebounds elastically. The impulse on the ball is :

Text Solution

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N.N is perpendicular to the inclined face. N.N is therefore the line of impact. `vec(PQ)` is direction of initial velocity of the ball.
`vec(QR)` is the direction of final velocity of the ball. Because this is an elastic collision,
`angle PQN.=angle N.QR= theta`
Impulse is measured along the impact line. The change in velocity of the ball along `NN.=Delta v = -2v cos theta` whereas there is no change in its velocity along the inclined plane.
`rArr` Impulse `= m Delta v = m (-2v cos theta)=-2mv cos theta`
Since the ball falls through a height h just before collision `v = sqrt(2gh)`
`rArr` Impulse `= - 2m cos theta sqrt(2gh)`
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