After a head-on elastic collision between two balls of equal masses,one is observed to have a speed of $3\,m/s$ along the positive $x$-axis and the other has a speed of $2\,m/s$ along the negative $x$-axis. What were the original velocities of the balls?

$A$ body $A$ of mass $m=0.1 \; kg$ has an initial velocity of $3 \hat{i} \; ms^{-1}$. It collides elastically with another body $B$ of the same mass which has an initial velocity of $5 \hat{j} \; ms^{-1}$. After the collision,$A$ moves with a velocity $\vec{v}_A = 4(\hat{i} + \hat{j}) \; ms^{-1}$. The energy of $B$ after the collision is written as $\frac{x}{10} \; J$. The value of $x$ is:

$A$ particle with kinetic energy $K = 3 \ J$ makes an elastic head-on collision with a stationary particle of twice its mass. Which of the following statements is correct?

$A$ smooth sphere $A$ moves on a frictionless horizontal surface with an angular velocity $\omega$ and a linear velocity $v$ of its center of mass. It undergoes an elastic collision with another identical sphere $B$ at rest. Neglecting friction everywhere,if the angular speeds after the collision are $\omega_A$ and $\omega_B$ respectively,then:

$A$ 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 $e = 0.5$.

$A$ neutron moving with velocity $u$ collides elastically with a stationary atom of mass number $A$. If the collision is head-on and the initial kinetic energy of the neutron is $E$, then the final kinetic energy of the neutron after the collision is: