$A$ gun fires a bullet of mass $50 \, g$ with a velocity of $30 \, m/s$. Because of this,the gun is pushed back with a velocity of $1 \, m/s$. The mass of the gun is .......... $kg$.

Two ice skaters $A$ and $B$ approach each other at right angles. Skater $A$ has a mass $30 \, kg$ and velocity $1 \, m/s$,and skater $B$ has a mass $20 \, kg$ and velocity $2 \, m/s$. They meet and cling together. Their final velocity of the couple is ............. $m/s$.

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 $L$. The velocity of the man with respect to ground $v_1$ will be

$A$ rifleman,who together with his rifle has a mass of $100\,kg$,stands on a smooth surface and fires $10$ shots horizontally. Each bullet has a mass of $10\,g$ and a muzzle velocity of $800\,ms^{-1}$. The velocity which the rifleman attains after firing $10$ shots is $..........\,ms^{-1}$.

$A$ body of mass $50 \, kg$ is projected vertically upwards with a velocity of $100 \, m/s$. After $5 \, s$,the body breaks into two pieces of mass $20 \, kg$ and $30 \, kg$. If the $20 \, kg$ piece travels upwards with a velocity of $150 \, m/s$,what is the velocity of the $30 \, kg$ block?

$A$ 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?