Suppose a ball is projected with speed `u` at an angle `alpha` with horizontal. It collides at some distance with a wall parallel to y-axis.
Let `v_(x)` and `v_(y)` be the components of its velocity along `x` and y-directions at the time of impact with wall. Coefficient of restitution between the ball and the wall is `e`. Component of its velocity along `y`-diection (common tangent) `v_(y)` will remain unchanged while component of its velocity along `x` -direction (common normal) `v_(x)` will become `ev_(x)` is opposite direction.

The situation shown in the figure a small ball is projected at an angle `alpha` between two vertical walls such that in the absence of the wall its range would have been `5d`. Given that all the collisions are perfectly elastic (for first and second problems), the walls are supposed to be very tall.
The total time taken by the ball to come back to the ground (if collision is inelastic) is

Options

A. `gt (2u sin alpha)/(g)`
B. `lt (2u sin alpha)/(g)`
C. `= (2u sin alpha)/(g)`
D. `= (2u cos alpha)/(g)`

Answer

C

Explanation

Vertical component of velocity of the ball do not change after collision.