Question

A ball of mass m approaches a wall of mass M (>> m) with the speed 4 m/s along normal to the wall. The speed of wall is 1m/s towards the ball . The speed of the ball after an elastic collision with the wall is-

• A. 5 m/s away from the wall
• B. 3 m/s away from the wall
• C. 9 m/s away from the wall
• D. 6 m/s away from the wall

Answer 1

The correct option is D 6 m/s away from the wall

$\text{Step 1: Initial \& final situation [Ref. Fig.]}$

Right direction is positive and left direction is negative.

$\text{Step 2: Apply law of restitution}$

Final velocity of wall be same as initial as $M>>>m$

Therefore $V_{wall}=-1m/s$

$e=\frac{V\left(seperation\right)}{V\left(approach\right)}$ (Along line of collision)

For elastic collision $e=1$

$\Rightarrow e=1=\left(\frac{V_{wall}-V_{ball}}{u_{ball}-u_{wall}}\right)$

$u_{wall}=-1m/s$

$u_{ball}=+4m/s$

$\Rightarrow 1=\left(\frac{-1-V_{ball}}{4+1}\right)\Rightarrow V_{ball}=-6m/s$

Negative sign means left direction (away from wall)

Hence option D is correct.