$A$ ball is dropped from a height of $5 \ m$ on a planet. It rebounds to a height of $1.8 \ m$. What is the fraction of velocity lost by the ball?

In an inelastic collision,after collision the kinetic energy

$A$ body falls freely from a height $h$ on a fixed horizontal plane and rebounds. If $e$ is the coefficient of restitution,the total distance travelled before it comes to rest is

$A$ bullet of mass $10 \,g$ moving with a speed of $20 \,m/s$ hits an ice block of mass $990 \,g$ kept on a frictionless floor and gets stuck in it. How much ice will melt if $50 \%$ of the lost kinetic energy $(KE)$ goes to the ice? (Initial temperature of the ice block and bullet $= 0^{\circ}C$,Latent heat of fusion of ice $L = 80 \,cal/g = 336 \,J/g$)

$A$ mass $m$ moves with a velocity $v$ and collides inelastically with another identical mass at rest. After the collision,the $1^{st}$ mass moves with velocity $\frac{v}{\sqrt{3}}$ in a direction perpendicular to the initial direction of motion. Find the speed of the $2^{nd}$ mass after the collision.

$A$ bullet of mass $m$ and speed $v$ hits a pendulum bob of mass $M$ at time $t_1$,and passes completely through the bob. The bullet emerges at time $t_2$ with a speed of $v/2$. The pendulum bob is suspended by a stiff rod of length $l$ and negligible mass. After the collision,the bob can barely swing through a complete vertical circle. At time $t_3$,the bob reaches the highest position. What quantities are conserved in this process?