Ball $A$ moving at $12 \ m/s$ collides elastically with ball $B$ at rest as shown in the figure. If both balls have the same mass,what is the final velocity of ball $A$ after the collision (in $m/s$)? (Assume the collision is two-dimensional and the angle of incidence is $60^\circ$ with the vertical axis).

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 $m/s$.

$A$ moving particle of mass $m$ makes a head-on elastic collision with another particle of mass $2m$ which is initially at rest. The percentage loss in energy of the colliding particle on collision is close to .................. $\%$

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.

Which of the following statements is true?

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 $\theta_{1}$.