An object of mass $M$ is much heavier than another object of mass $m$. The heavy object moving with speed $v$ undergoes an elastic collision with the light object at rest. What will be the speed of the light object after the collision?

The rebound coefficient between a tennis ball and a racket is defined as $e = v_2/v_1$,where $v_1$ is the incoming speed of the ball and $v_2$ is the speed of the ball after rebound while the racket is at rest. $A$ tennis ball falls from height $H$ to a racket at rest and bounces back to $0.8 H$. $A$ tennis player is using the racket to hit an incoming tennis ball traveling at $150 \ km/hr$ and the racket is moving at $100 \ km/hr$ towards the ball. What is the speed of the ball after being hit? (Assume the mass of the racket $\gg$ that of the ball).

$A$ sphere of mass $10 \ kg$ moving with a velocity of $10 \ m/s$ undergoes an elastic collision with a body of mass $5 \ kg$ moving in the same direction with a velocity of $4 \ m/s$. What are their velocities after the collision?

$Assertion$ : In an elastic collision of two billiard balls,the total kinetic energy is conserved during the short time of oscillation of the balls (i.e.,when they are in contact).
$Reason$ : Energy spent against friction does not follow the law of conservation of energy.

Two balls of mass $5 \ kg$ are moving in opposite directions with the same speed of $5 \ m/s$. They undergo a head-on elastic collision. Find the final velocity of the balls in $m/s$.

$A$ billiard table has length and width as shown in the figure. $A$ ball is placed at point $A$. At what angle $\theta$ should the ball be projected so that after colliding with two walls,the ball will fall into the pocket $B$? Assume that all collisions are perfectly elastic and neglect friction.