$A$ body falls freely from a height of $100 \ m$ onto the ground and rebounds to a maximum height of $36 \ m$ after collision. The coefficient of restitution between the ground and the body is

$A$ smooth sphere moves on a horizontal surface with a velocity vector $2\hat{i} + 2\hat{j}$ before it strikes a vertical wall. The wall is parallel to the $\hat{j}$ vector,and the coefficient of restitution between the sphere and the wall is $e = 1/2$. What will be the velocity vector of the sphere after it strikes the wall?

$A$ ball is dropped from a height of $20 \ m$. If it loses $20\%$ of its energy upon collision with the ground,what is the coefficient of restitution?

$A$ metal ball falls from a height of $32 \ m$ on a steel plate. If the coefficient of restitution is $0.5$,to what height will the ball rise after the second bounce?

$A$ 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?

$A$ moving ball collides head-on with a similar ball at rest. If $\frac{1}{4}$ of the kinetic energy is lost during the impact,the value of the coefficient of restitution is: