$A$ ball is dropped from a height of $20 \, cm$. The ball rebounds to a height of $10 \, cm$. What is the percentage loss of energy? ................ $\%$

$A$ particle of mass $m$ is projected from the ground with an initial speed $u_0$ at an angle $\alpha$ with the horizontal. At the highest point of its trajectory,it makes a completely inelastic collision with another identical particle,which was thrown vertically upward from the ground with the same initial speed $u_0$. The angle that the composite system makes with the horizontal immediately after the collision is :

$A$ block of mass '$m$' moving on a frictionless horizontal surface collides with a spring of spring constant '$K$' and compresses it through a distance '$x$'. The maximum momentum of the block after collision is

$A$ free body of mass $8 \, kg$ is travelling at $2 \, m/s$ in a straight line. At a certain instant,the body splits into two equal parts due to an internal explosion which releases $16 \, J$ of energy. Neither part leaves the original line of motion. Finally:

$A$ boat of mass $1000 \,kg$ goes from rest to a speed of $20.0 \,m/s$ in $5.0 \,s$. The water exerts a constant drag force and the acceleration of the boat is constant. If the average power required by the boat is $45000 \,W$, then the magnitude of the drag force is: (in $\,N$)

$A$ block of weight $10 \ N$ slides down a curved track $AB$ and then onto a rough horizontal surface. The coefficient of kinetic friction between the block and the rough surface is $0.20$. If the block starts sliding from a height of $1.0 \ m$ above the horizontal surface,calculate the distance $S$ it travels on the rough surface before coming to rest. [$g = 10 \ m \ s^{-2}$]