Question

A particle of mass m moves with velocity $V_0=20$ $m/sec$ towards a large wall of same mass that is moving with velocity $V=5m/sec.$ towards the particle as shown. If the particle collides with the wall elastically, the speed of the particle just after the collision is:

• A. 30 m/s
• B. 20 m/s
• C. 25 m/s
• D. 22 m/s

Answer 1

The correct option is B 20 m/s

When the ball collides with the wall,an impulse is provided by the wall to the ball,and vice versa.

Let a normal reaction $N$ be provided to the ball.

Let the velocity of ball after collision be $v_b$

Let the velocity of wall after collision be $v_w$

$\int$$Ndt=m(v_b-v_o)$

$-\int$$Ndt=m(v_b+v)$

From these two equations,we get $v_w+v_b=v_o-v=15m{s}^{-1}............\left(|\right)$

Kinetic Energy is conserved for elastic collision :

$m{v_o}^2+m{v}^2=m{v_b}^2+m{v_w}^2$

Solving this equations with the help of (|)

we get $v_b=20m{s}^{-1}or-5m{s}^{-1}$