$A$ body is dropped on the ground from a height $h_1$ and after hitting the ground,it rebounds to a height $h_2$. If the ratio of velocities of the body just before and after hitting the ground is $4$,then the percentage loss in kinetic energy of the body is $\frac{x}{4}$. The value of $x$ is $.......$

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:

If the coefficient of restitution is $0.5$,what is the percentage loss of energy on each rebounding of a ball dropped from a height?

$A$ body of mass $m$ moving with velocity $v$ collides inelastically with another body of the same mass. After the collision,the first body moves with velocity $\frac{v}{\sqrt{3}}$ in a direction perpendicular to the initial direction of motion. What will be the speed of the second body after the collision?

$A$ metal ball falls from a height of $32 \ m$ on a steel plate. If the coefficient of restitution is $0.5$,to what height will the ball rise after the second bounce?

$A$ smooth sphere moves on a horizontal surface with a velocity vector $2\hat{i} + 2\hat{j}$ before it strikes a vertical wall. The wall is parallel to the $\hat{j}$ vector,and the coefficient of restitution between the sphere and the wall is $e = 1/2$. What will be the velocity vector of the sphere after it strikes the wall?