$A$ ball kept at $20 \,m$ height falls freely in a downward direction vertically and hits the ground. The coefficient of restitution is $0.4$. After the first rebound, the upward velocity is $[g = 10 \,m/s^2]$. (in $\,m/s$)

The sphere $A$ of mass $m$ moving with a constant velocity hits another sphere $B$ of mass $2m$ at rest. If the coefficient of restitution is $0.4$,the ratio of the velocities of the spheres $A$ and $B$ after collision is

$A$ tennis ball hits the floor with a speed $v$ at an angle $\theta$ with the normal to the floor. If the collision is inelastic and the coefficient of restitution is $\varepsilon$, what will be the angle of reflection?

$A$ ball is moving with velocity $4 \ m/s$ and collides head-on with another stationary ball of double the mass. If the coefficient of restitution is $0.2$,then their velocities (in $m/s$) after the collision will be:

$A$ glass ball collides with a smooth horizontal surface with a velocity $\vec{v} = a \hat{i} - b \hat{j}$. If the coefficient of restitution of the collision is $e$,find the velocity of the ball just after the collision. ($x$-axis is along the ground and $y$-axis is along the vertical).

$A$ bullet of mass $0.01\, kg$ travelling at a speed of $500\, m/s$ strikes and passes horizontally through a block of mass $2\, kg$ which is suspended by a string of length $5\, m$. The centre of gravity of the block is found to rise a vertical distance of $0.1\, m$. What is the speed of the bullet after it emerges from the block? (The time of passing of the bullet is negligible,$g = 9.8\, m/s^2$)