There is a head-on elastic collision between two particles moving in the same direction with speeds $5 \,m/s$ and $3 \,m/s$ respectively. After the collision,the velocity of the first particle becomes $4 \,m/s$ in the same direction. What is the velocity of the second particle?

$A$ moving body with mass $m_1$ strikes a stationary mass $m_2$. What should be the ratio $\frac{m_1}{m_2}$ so as to decrease the velocity of the first body by $1.5$ times after the collision?

$A$ 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,

$A$ ball of mass $m$ moving with velocity $v$ undergoes an elastic collision with another ball of the same mass $m$ moving in the opposite direction with velocity $2v$. What will be their velocities after the collision?

$A$ ball initially at rest is hit by another identical ball moving with some velocity as shown. Find the angle $\theta_2$ if the surface is without friction and the collision is perfectly elastic. $......^{\circ}$

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).