A ball of negligible size and mass `m` is given a velocity `v_0` on the centre of the cart which has a mass M and is originally at rest. If the coefficient of restitution between the ball and walls A and B is e. Determine the velocity of the ball and the cart just after the ball strikes A. Also, determine the total time needed for the ball to strike A, rebound, then strike B, and rebound and then return to the centre of the cart. Neglect friction.

Answer

A, B, C, D

Explanation

Applying conservation of linear momentum and

`e=("Relative speed of separation")/("Relative speed of approach") , we get
`mv_0=Mv_2-mv_1` …(i)
`v_1+v_2=ev_0` …(ii)
Solving these two equations, we get,
`v_1=((eM-m)/(M+m))v_0`, `v_2=m((e+1)/(M+m))v_0`
The desired time is
`t=(d)/(v_0)+(2d)/(ev_0)+(d)/(e^2v_0)`
or `t=(d)/(v_0)(1+2/e+1/e^(2))`