$A$ 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 $..........\,ms^{-1}$.

$A$ cannon shell fired breaks into two equal parts at its highest point. If one part retraces its path to the cannon with kinetic energy $E_1$ and the kinetic energy of the second part is $E_2$,then

An explosion breaks a rock into three parts in a horizontal plane. Two of them go off at right angles to each other. The first part of mass $1 \, kg$ moves with a speed of $12 \, m s^{-1}$ and the second part of mass $2 \, kg$ moves with $8 \, m s^{-1}$ speed. If the third part flies off with $4 \, m s^{-1}$ speed,then its mass is ......... $kg$.

Three particles of masses $10\;g, 20\;g$ and $40\;g$ are moving with velocities $10\hat{i}, 10\hat{j}$ and $10\hat{k}\;m/s$ respectively. If due to some mutual interaction,the first particle comes to rest and the velocity of the second particle becomes $(3\hat{i} + 4\hat{j})\;m/s$,then the velocity of the third particle is

$A$ cannon ball is fired with a velocity $200 \, m/s$ at an angle of $60^{\circ}$ with the horizontal. At the highest point of its flight,it explodes into $3$ equal fragments. One fragment goes vertically upwards with a velocity $100 \, m/s$,and the second one falls vertically downwards with a velocity $100 \, m/s$. The third fragment will be moving with a velocity:

$A$ body of mass $M$ moving with velocity $V$ explodes into two equal parts. If one part comes to rest and the other part moves with velocity $v_{0}$,what would be the value of $v_{0}$?