$A$ man fires a bullet of mass $200 \,g$ at a speed of $5 \,m/s$. The gun has a mass of $1 \,kg$. With what velocity does the gun recoil backwards?

If a shell fired from a cannon explodes in mid-air,then:

An explosion blows a stationary rock into three parts. Two parts of masses $1 \,kg$ and $2 \,kg$ move at right angles to one another with velocities $12 \,ms^{-1}$ and $8 \,ms^{-1}$, respectively. If the velocity of the third part is $4 \,ms^{-1}$, the mass of the rock is (in $\,kg$)

The figure shows a man of mass $m$ standing at the end $A$ of a trolley of mass $M$ placed at rest on a smooth horizontal surface. The man starts moving towards the end $B$ with a velocity $u_{rel}$ with respect to the trolley. The length of the trolley is $L$. When the man starts moving,then the velocity of the trolley $v_2$ with respect to ground will be

Two persons of mass $m_1$ and $m_2$ are standing at the two ends $A$ and $B$ respectively,of a trolley of mass $M$ as shown. When only the person standing at $B$ jumps from the trolley towards the right while the person at $A$ keeps standing,then

$A$ projectile moving vertically upwards with a velocity of $200\, ms^{-1}$ breaks into two equal parts at a height of $490\, m$. One part starts moving vertically upwards with a velocity of $400\, ms^{-1}$. How much time will it take,after the break up,for the other part to hit the ground? .............. $s$