$A$ ball is dropped from a height of $20 \ m$. If it loses $20\%$ of its energy upon collision with the ground,what is the coefficient of restitution?

$A$ rubber ball is released from a height of $5\, m$ above the floor. It bounces back repeatedly,always rising to $\frac{81}{100}$ of the height through which it falls. Find the average speed of the ball. (Take $g = 10\, m/s^2$)

Ball $P$ of mass $m$ moving with velocity $v$ collides with another ball $Q$ of mass $2m$, which is at rest. If $v_P$ and $v_Q$ are the final velocities of $P$ and $Q$ respectively after the collision, then (Assume the coefficient of restitution is $e = 1/3$):

Two identical balls $P$ and $Q$ moving in the $x-y$ plane collide at the origin $(x=0, y=0)$ of the coordinate system. Their velocity components just before the moment of impact were,for ball $P$,$v_x = 6 \ m/s, v_y = 0$; for ball $Q$,$v_x = -5 \ m/s, v_y = 2 \ m/s$. As a result of the collision,ball $P$ comes to rest. The velocity components of ball $Q$ just after the collision will be:

$A$ body moving along a straight line collides with another body of the same mass moving in the same direction with half of the velocity of the first body. If the coefficient of restitution between the two bodies is $0.5$,then the ratio of the velocities of the two bodies after collision is (treat the collision as one dimensional).

$A$ particle falls from a height $h$ upon a fixed horizontal plane and rebounds. If $e$ is the coefficient of restitution,the total distance travelled before rebounding has stopped is