$A$ ball of mass $m$ moving with velocity $V$ makes a head-on elastic collision with a ball of the same mass moving with velocity $2V$ towards it. Taking the direction of $V$ as positive,the velocities of the two balls after the collision are:

$STATEMENT-1$: In an elastic collision between two bodies, the relative speed of the bodies after collision is equal to the relative speed before the collision. Because
$STATEMENT-2$: In an elastic collision, the linear momentum of the system is conserved.

$A$ neutron makes a head-on elastic collision with a stationary deuteron. The fractional energy loss of the neutron in the collision is

$A$ billiard table has length and width as shown in the figure. $A$ ball is placed at point $A$. At what angle $\theta$ should the ball be projected so that after colliding with two walls,the ball will fall into the pocket $B$? Assume that all collisions are perfectly elastic and neglect friction.

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.

Consider the situation as shown in the figure. The ball strikes the wall normally and the collision is elastic. The wall is moving with a velocity of $20 \ m/s$ to the right,and the ball is moving with a velocity of $10 \ m/s$ to the left. The mass of the ball is $500 \ g$. The change in the kinetic energy of the ball is $....J$.