$A$ $1 \,kg$ ball moving at $12 \,ms^{-1}$ collides with a $2 \,kg$ ball moving in the opposite direction at $24 \,ms^{-1}$. If the coefficient of restitution is $2/3$, then their velocities after the collision are

$A$ small ball falling vertically downward with a constant velocity of $4 \ m/s$ strikes elastically a massive inclined cart moving with a velocity of $4 \ m/s$ horizontally,as shown in the figure. The velocity of the rebound of the ball is

An object of mass $m$ moving with velocity $u$ collides with another stationary object of mass $M$ and stops just after the collision. The coefficient of restitution is

$A$ tennis ball is released from height $h$ above ground level. If the ball makes an inelastic collision with the ground,to what height will it rise after the third collision?

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:

$A$ smooth sphere is moving on a horizontal surface with velocity vector $3 \hat{i} + \hat{j}$ immediately before it hits a vertical wall. The wall is parallel to the $\hat{j}$ vector,and the coefficient of restitution between the wall and the sphere is $\frac{1}{3}$. What is the velocity vector of the sphere after it hits the wall?