$A$ 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?

Consider the following statements $A$ and $B$ and identify the correct answer:
$A$. In an elastic collision,if a body suffers a head-on collision with another of the same mass at rest,then the first body comes to rest while the other starts moving with the velocity of the first one.
$B$. Two bodies of equal mass suffering a head-on elastic collision merely exchange their velocities.

$A$ body $A$ of mass $4m$ moving with speed $u$ collides with another body $B$ of mass $2m$,which is at rest. The collision is head-on and elastic in nature. After the collision,the fraction of energy lost by the colliding body $A$ is

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 $\theta_{1}$.

Ball $A$ moving at $12 \ m/s$ collides elastically with ball $B$ (initially at rest) as shown in the figure. If both balls have the same mass, what is the final velocity of ball $A$ in $m/s$?

Explain the special cases of elastic collision in one dimension.