A ball is projected from the ground with speed u at an angle alphawith 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.

A ball is projected from the ground with speed u at an angle alphawith

1.	A ball is projected from the ground with speed u at an angle alphawith 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.
Answer» SOLUTION :As we have discussed in the theory, the horizontal component of the velocity of BALL during the path OAB is `u cos alpha ` while in its return journey BCO it is `eu coa alpha.` FTHE time of fight T also remains unchanged. Hence, `T = t _(OAB)+ t _(BCO) or (2 u sin alpha )/( g) = (a)/( u cos alpha ) + (a)/( eu cos alpha )` (or) `(a)/( eu cos alpha ) = (2 u sin alpha )/(g ) (a)/( ucos alpha )` (or )` (a )/( eu cos alpha ) = (2u ^(2) sin alpha cos alpha - ag)/(gu cos alpha)` `therefore e = (ag)/( 2u ^(2) sin alpha cos alpha - ag ) or e = (1)/(( ( u ^(2) sin 2 alpha )/( ag )-1))`