A ball strikes against the floor and returns with double the velocity; in which type of collision is it possible?

A bullet of mass $0.012\;kg$ and hortzontal speed $70\; m s ^{-1}$ strikes a block of wood of mass $0.4\; kg$ and instantly comes to rest with respect to the block. The block is suspended from the celling by means of thin wires. Calculate the height to which the block rises. Also, estimate the amount of heat produced in the block.

A projectile of mass $3m$ is moving at $40\, m/s$ at is highest point, where it breaks into two parts $m$ and $2m$. Mass $2m$ moves vertically up at $25\, m/s$. The other part will move at speed  .................... $\mathrm{m}/ \mathrm{s}$

Two particles $A$ and $B,$ move with constant  velocities $\vec v_1$ and $\vec v_2$. At the initial moment their position vectors are $\vec r_1$ and $\vec r_2$ respectively. The condition for particles $A$ and $B$ for their collision is

A body of mass m having an initial velocity $v$, makes head on collision with a stationary body of mass $M$. After the collision, the body of mass $m$ comes to rest and only the body having mass $M$ moves. This will happen only when

A steel ball of radius $2\, cm$ is at rest on a frictionless surface. Another ball of radius $4\,cm$ moving at a velocity of $81 \,cm/sec$ collides elastically with first ball. After collision the smaller ball moves with speed of ............. $\mathrm{cm} / \mathrm{sec}$