$A$ man of $60\,kg$ is running on the road and suddenly jumps into a stationary trolley car of mass $120\,kg$. Then,the trolley car starts moving with a velocity of $2\,ms^{-1}$. The velocity of the running man when he jumped into the car was . . . . . . $ms^{-1}$.

$A$ spacecraft of mass $M$ is moving with velocity $V$ and suddenly explodes into two pieces. $A$ part of it of mass $m$ comes to rest. The velocity of the other part will be:

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:

$A$ projectile of mass $m$ is projected from ground with a speed of $50 \, m/s$ at an angle of $53^{\circ}$ with the horizontal. It breaks up into two equal parts at the highest point of the trajectory. One particle comes to rest immediately after the explosion. The distance between the pieces of the projectile when they reach the ground is: (in $, m$)

$A$ ball is projected at $60^{\circ}$ from the horizontal at $200 \, m/s$. At the maximum height during its flight,it explodes into $3$ equal fragments. Out of these,one part travels at $100 \, m/s$ vertically up while another travels at $100 \, m/s$ vertically down. What will be the speed of the third part just after the explosion?

$A$ 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