$A$ ball is thrown with a velocity of $6\, m/s$ vertically downwards from a height $H = 3.2\, m$ above a horizontal floor. If it rebounds back to the same height,then the coefficient of restitution $e$ is $[g = 10\, m/s^2]$.

$A$ 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).

$A$ ball of mass $M$ falls from a height $h$ on a floor. If the coefficient of restitution is $e$,the height attained by the ball after two rebounds is

$A$ ball is dropped from a height $h$. It bounces repeatedly. Find the height attained by the ball after $n$ bounces and the time taken by the ball to complete $n$ bounces.

Two bodies having same mass $40\, kg$ are moving in opposite directions,one with a velocity of $10\, m/s$ and the other with $7\, m/s$. If they collide and move as one body,the velocity of the combination is ........ $m/s$.

$A$ body of mass $m_1$ moving with a velocity $3 \, ms^{-1}$ collides with another body at rest of mass $m_2$. After the collision,the velocities of the two bodies are $2 \, ms^{-1}$ and $5 \, ms^{-1}$ respectively along the direction of motion of $m_1$. The ratio $\frac{m_1}{m_2}$ is: