$A$ 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?

$A$ particle of mass $m$ strikes the ground inelastically with a coefficient of restitution $e$. Find the relation between the angles $\theta$ and $\alpha$ as shown in the figure.

Two pendulums with identical bobs and lengths are suspended from a common support such that in rest position the two bobs are in contact (figure). One of the bobs is released after being displaced by $10^{\circ}$ so that it collides elastically head-on with the other bob.
$(a)$ Describe the motion of two bobs.
$(b)$ Draw a graph showing variation in energy of either pendulum with time,for $0 \leqslant t \leqslant 2T$,where $T$ is the period of each pendulum.

$A$ ball is dropped from a height $h$ on a floor of coefficient of restitution $e$. The total distance covered by the ball just before the second hit is

$A$ 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).

Two solid rubber balls $A$ and $B$ having masses $200 \, g$ and $400 \, g$ respectively are moving in opposite directions. The velocity of $A$ is $0.3 \, m/s$. After the collision,both balls come to rest. Determine the velocity of $B$ in $m/s$.