$A$ ball is dropped from a height $h$. As it bounces off the floor,its speed is $80$ percent of what it was just before it hit the floor. The ball will then rise to a height of most nearly .............. $h$.

$A$ ball is moving with speed $20 \, m/s$ collides with a smooth surface as shown in the figure. The magnitude of the change in velocity of the ball will be ........... $m/s$.

$A$ ball falls freely from rest from a height of $6.25 \ m$ onto a hard horizontal surface. If the ball reaches a height of $81 \ cm$ after the second bounce from the surface,the coefficient of restitution is

$A$ $2 \,kg$ ball moving at $24 \,ms^{-1}$ undergoes inelastic head-on collision with a $4 \,kg$ ball moving in the opposite direction at $48 \,ms^{-1}$. If the coefficient of restitution is $2/3$, their velocities in $ms^{-1}$ after impact are

$A$ 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).

$A$ large ball of mass $M$,moving with velocity $u$,strikes a small ball of mass $m$,which is at rest. After the collision,the small ball attains velocity $u$ and the large ball attains velocity $v$. What is the value of $v$?