Two balls at the same temperature collide. What is conserved?

$A$ ball loses $15.0\%$ of its kinetic energy when it bounces back from a concrete wall. With what speed must you throw it vertically down from a height of $12.4\, m$ to have it bounce back to the same height (ignore air resistance)? ............. $m / s$

$A$ block of mass $1 \ kg$ is placed at point $A$ on a rough path. It is gently pushed to the right. It slides down the slope and reaches point $B$. Find the work done by the friction force on the block during the journey from point $A$ to point $B$ in $J$. (Assume the vertical height difference between $A$ and $B$ is $0.2 \ m$ and the block starts and ends at rest).

$A$ particle of mass $3 \ kg$ is moved slowly along the path $ABCDE$ from $A$ to $E$. The heights of $B$,$C$,and $D$ are $5 \ m$,$4 \ m$,and $6 \ m$ respectively. The total path length is $20 \ m$,the horizontal distance $AE = 10 \ m$,and the coefficient of friction $\mu = 0.6$. Calculate the work done in $J$ to slowly move the mass from $A$ to $E$. (Take $g = 10 \ m/s^2$)

Two bodies $A$ and $B$ of masses $1.5 \ kg$ and $3 \ kg$ are moving with velocities $20 \ m \ s^{-1}$ and $15 \ m \ s^{-1}$ respectively. If the same retarding force is applied on the two bodies,then the ratio of the distances travelled by the bodies $A$ and $B$ before they come to rest is

$A$ ball of mass $2 \,kg$ is thrown from a tall building with velocity $v = (20 \,m/s) \hat{i} + (24 \,m/s) \hat{j}$ at time $t = 0 \,s$. The change in the potential energy of the ball after $t = 8 \,s$ is (The ball is assumed to be in air during its motion between $0 \,s$ and $8 \,s$, $\hat{i}$ is along the horizontal and $\hat{j}$ is along the vertical direction. Take $g = 10 \,m/s^2$). (in $\,kJ$)