$A$ ball is dropped from a height of $20 \ m$. If it loses $20\%$ of its energy upon collision with the ground,what is the coefficient of restitution?

Two particles of masses $m_1$ and $m_2$ move with initial velocities $u_1$ and $u_2$. On collision,one of the particles gets excited to a higher level after absorbing energy $\varepsilon$. If the final velocities of the particles are $v_1$ and $v_2$,then we must have:

$A$ ball moving with a velocity $v$ collides head-on with a stationary second ball of the same mass. After the collision, the velocity of the first ball is reduced to $0.15 v$. The kinetic energy of the system is decreased nearly by (in $\%$)

$A$ sphere collides with another sphere of identical mass. After collision,the two spheres move. The collision is inelastic. Then the angle between the directions of the two spheres is

Two identical balls $A$ and $B$ of equal mass $m$ are lying on a smooth surface as shown in the figure. If ball $A$ hits ball $B$ at rest with a velocity $16 \,ms^{-1}$,then the coefficient of restitution $e$ between $A$ and $B$ so that $B$ just reaches the highest point of the smooth inclined plane of height $5 \,m$ is $\left(g=10 \,ms^{-2}\right)$

An inelastic ball is dropped from a height of $100\, m$. Due to the impact,$20\%$ of its energy is lost. To what height will the ball rise?