A ball of mass `m` is projected with a velocity `'u'` at angle `theta` with the horizontal. It collides with a smooth box of mass `'M'` at its highest position. If the co-efficient of restitution is `'e'`.

Find the horizontal distance travelled by the ball before collision.

Options

A. `(u^(2) 2 sin theta cos theta)/(g)`
B. `(u^(2) sin theta cos theta)/(g)`
C. `(u^(2) sin theta cos theta)/(2g)`
D. `(u^(2) sin theta cos theta)/(4g)`

Answer

B

Explanation

Recoil velocity of ball after collision `v ((m-eM)/(M+m))u cos theta`
From `v_(1) = ((M_(1)-eM_(2))/(M_(1)+m_(2)))+(2m_(2)u_(2))/(m_(1)+m_(2))`
`(R')/(R ) = (v)/(u cos theta) = ((eM-m)/(M+m)), R' = ((eM-m)/(M+m))R`
The ball hit at a point `'P'` at a distance
`Delta x = R-R' = R(1-((eM-m)/(M+m)))`
`=R((M(1-e)+2m)/(M+m))`