$A$ mass $M$ moving with a certain speed $V$ collides elastically with another stationary mass $m$. After the collision,the masses $M$ and $m$ move with speeds $V^{\prime}$ and $v$,respectively. All motion is in one dimension. Then,

Explain the special cases of elastic collision in one dimension.

Two perfectly elastic particles $P$ and $Q$ of equal mass are travelling along the line joining them with velocities $15 \ m/s$ and $10 \ m/s$ respectively. After a perfectly elastic collision,their velocities (in $m/s$) will be:

On a frictionless surface,a block of mass $M$ moving at speed $V$ collides elastically with another block of same mass $M$ which is initially at rest. After collision,the first block moves at an angle $\theta$ to its initial direction and has a speed $\frac{V}{3}$. The second block's speed after the collision is:

$A$ particle with kinetic energy $K = 3 \ J$ makes an elastic head-on collision with a stationary particle of twice its mass. Which of the following statements is correct?

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).