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 ............. $m/s$.

$A$ shell is fired from a cannon with a velocity $V$ at an angle $\theta$ with the horizontal direction. At the highest point in its path,it explodes into two pieces of equal masses. One of the pieces comes to rest. The speed of the other piece immediately after the explosion is

$A$ shell of mass $0.020 \; kg$ is fired by a gun of mass $100 \; kg$. If the muzzle speed of the shell is $80 \; m s^{-1}$,what is the recoil speed in $m/s$ of the gun?

$A$ stationary body explodes into two parts of masses $M_{1}$ and $M_{2}$. They move in opposite directions with velocities $v_{1}$ and $v_{2}$. The ratio of their kinetic energies is

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

$A$ man weighing $80 \, kg$ is standing in a trolley weighing $320 \, kg$. The trolley is resting on frictionless horizontal rails. If the man starts walking on the trolley with a speed of $1 \, m/s$ relative to the trolley,then after $4 \, s$ his displacement relative to the ground will be ........ $m$.