$A$ man (mass $= 50\, kg$) and his son (mass $= 20\, kg$) are standing on a frictionless surface facing each other. The man pushes his son so that he starts moving at a speed of $0.70\, ms^{-1}$ with respect to the man. The speed of the man with respect to the surface is ........ $ms^{-1}$

$A$ bomb at rest explodes into three pieces of equal masses. If two pieces move perpendicular to each other,each with a speed $v$,then the speed of the third piece is:

$12 \,kg$ bomb at rest explodes into two pieces of $4 \,kg$ and $8 \,kg$. If the momentum of the $4 \,kg$ piece is $20 \,Ns$, what is the kinetic energy of the $8 \,kg$ piece (in $\,J$)?

An open water-tight railway wagon of mass $5 \times 10^3 \text{ kg}$ coasts at an initial velocity $1.2 \text{ m/s}$ without friction on a railway track. Rain drops fall vertically downwards into the wagon. The velocity of the wagon after it has collected $10^3 \text{ kg}$ of water will be .............. $\text{m/s}$.

$A$ shell at rest at the origin explodes into three fragments of masses $1 \ kg$,$2 \ kg$,and $m \ kg$. The $1 \ kg$ and $2 \ kg$ pieces fly off with speeds of $5 \ m/s$ along the $x$-axis and $6 \ m/s$ along the $y$-axis,respectively. If the $m \ kg$ piece flies off with a speed of $6.5 \ m/s$,the total mass of the shell must be ......... $kg$.

$A$ body of mass $0.25 \, kg$ is projected with a muzzle velocity of $100 \, m/s$ from a tank of mass $100 \, kg$. What is the recoil velocity of the tank in $m/s$?