After a head-on elastic collision between two balls of equal masses,one is observed to have a speed of $3 \, m/s$ along the positive $x$-axis and the other has a speed of $2 \, m/s$ along the negative $x$-axis. The original velocities of the balls are:

Five identical elastic balls are suspended in a row with strings of equal length such that the distance between the sides of the balls is very small. If the ball at the right end is released from one side,then:

$A$ neutron with velocity $v$ strikes a stationary deuterium atom. By what factor does its kinetic energy change?

Consider the collision depicted in the figure to be between two billiard balls with equal masses $m_{1} = m_{2}$. The first ball is called the cue, while the second ball is called the target. The billiard player wants to 'sink' the target ball in a corner pocket, which is at an angle $\theta_{2} = 37^{\circ}$. Assume that the collision is elastic and that friction and rotational motion are not important. Obtain $\theta_{1}$.

$A$ body of mass $m_1$ undergoes a perfectly elastic collision with a stationary body of mass $m_2$. If the velocity of mass $m_1$ becomes $1/1.5$ times its initial velocity,find the ratio $\frac{m_1}{m_2}$.

An object $A$ of mass $20 \ kg$ and travelling at $20 \ m \ s^{-1}$ crashes into another object $B$ of mass $200 \ kg$ and travelling at $10 \ m \ s^{-1}$,in the same direction. After the collision,object $A$ bounces back in the opposite direction at a speed of $10 \ m \ s^{-1}$. The speed of the object $B$ after the collision is: (in $m \ s^{-1}$)