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A ball is projected from the ground with...

A ball is projected from the ground with speed u at an angle `alpha` with horizontal. It collides with a wall at a distance a from the point of projection and returns to its original position. Find the coefficient of restitution between the ball and the wall.

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The correct Answer is:
A, B
As we have discussed in the theory, the horizontal component of the velocity of ball duing the path OAB is `u cos alpha` while in its return jouney BCO it is `eu cos alpha`. The time of flight T also remains unchanged. Hence,
`T=t_(OAB)+t_(BCO)`
or `(2usin alpha)/(g)=(a)/(u cos alpha)+(a)/(eu cos alpha)`
`(a)/(eu cos alpha)=(2u^2sin alpha cos alpha-ag)/(gu cos alpha)`
`e=(ag)/(2u^2sin alpha cos alpha-ag)`
or `e=(1)/(((u^2sin 2alpha)/(ag)-1))`
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