$A$ ball of mass $m$ moving with a velocity of $9 \ m/s$ collides with another ball of the same mass $m$ at rest. After the collision,both balls move at an angle of $30^\circ$ with the original direction of motion. Find the velocity $v$ of both balls after the collision. (in $m/s$)

$A$ 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?

$A$ ball is dropped from a height $h$. It bounces repeatedly off the ground. What is the total distance covered by the ball before it comes to rest?

$A$ body moving along a straight line collides with another body of the same mass moving in the same direction with half of the velocity of the first body. If the coefficient of restitution between the two bodies is $0.5$,then the ratio of the velocities of the two bodies after collision is (treat the collision as one dimensional).

In the figure shown,a small ball hits obliquely a smooth and horizontal surface with speed $u$ whose $x$ and $y$ components are indicated. If the coefficient of restitution is $\frac{1}{2}$,then its $x$ and $y$ components $v_x$ and $v_y$ just after collision are respectively

$A$ 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