$A$ ball is dropped from a height of $80 \ m$ on a surface which is at rest. Find the height attained by the ball after the $2^{nd}$ collision if the coefficient of restitution is $e = 0.5$.

Six identical balls are lined in a straight groove made on a horizontal frictionless surface as shown. Two similar balls each moving with a velocity $v$ collide elastically with the row of $6$ balls from the left. What will happen?

What happens when two identical bodies moving in opposite directions undergo a perfectly elastic collision?

$A$ ball of mass $m$ moving with speed $u$ undergoes a head-on elastic collision with a stationary ball of mass $nm$. What is the fraction of the kinetic energy transferred to the heavier ball?

$A$ particle of mass $m$ moving with velocity $u$ makes an elastic one-dimensional collision with a stationary particle of mass $m$. They are in contact for a very short time $T$. Their force of interaction increases from zero to $F_0$ linearly in time $T/2$, and decreases linearly to zero in further time $T/2$. The magnitude of $F_0$ is

$A$ particle of mass $m$ with an initial velocity $u\hat{i}$ collides perfectly elastically with a mass $3m$ at rest. It moves with a velocity $v\hat{j}$ after collision. Then, $v$ is given by: