$A$ ball falls freely from a height $h$ on a rigid horizontal plane. If the coefficient of restitution is $e$,then the total distance travelled by the ball before hitting the plane the second time is

$A$ body falling from a height of $10\,m$ rebounds from a hard floor. If it loses $20\%$ of its energy in the impact,then the coefficient of restitution is:

$A$ ball is allowed to fall freely from a height of $42 \ m$ from the ground. If the coefficient of restitution between the ball and the ground is $0.4$,then the total distance travelled by the ball before it comes to rest is (in $m$)

$A$ smooth sphere is moving on a horizontal surface with velocity vector $3 \hat{i} + \hat{j}$ immediately before it hits a vertical wall. The wall is parallel to the $\hat{j}$ vector,and the coefficient of restitution between the wall and the sphere is $\frac{1}{3}$. What is the velocity vector of the sphere after it hits the wall?

Hail stones are observed to strike the surface of a frozen lake at $30^{\circ}$ with the vertical and rebound at $60^{\circ}$ with the vertical. Assuming the contact to be smooth,the coefficient of restitution is

$A$ ball $P$ of mass $0.5 \ kg$ moving with a velocity of $10 \ ms^{-1}$ collides with another ball $Q$ of mass $1 \ kg$ at rest. If the coefficient of restitution is $0.4$,the ratio of the velocities of the balls $P$ and $Q$ after the collision is