$A$ 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:

$A$ man of $50 \,kg$ is standing at one end of a boat of length $25 \,m$ and mass $200 \,kg$. If he starts running and when he reaches the other end, he has a velocity $2 \,ms^{-1}$ with respect to the boat. The final velocity of the boat is: (in $ms^{-1}$)

In an explosion,a body breaks up into two pieces of unequal masses. In this process:

$A$ 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

$A$ projectile is fired with velocity $u$ at an angle $\theta$ with the horizontal. At the highest point of its trajectory,it splits into three segments of masses $m, m$,and $2m$. The first part falls vertically downward with zero initial velocity,and the second part returns via the same path to the point of projection. The velocity of the third part of mass $2m$ just after the explosion will be:

$A$ trolley of mass $200\; kg$ moves with a uniform speed of $36\; km/h$ on a frictionless track. $A$ child of mass $20\; kg$ runs on the trolley from one end to the other ($10\; m$ away) with a speed of $4\; m/s$ relative to the trolley in a direction opposite to its motion,and jumps out of the trolley. What is the final speed of the trolley? How much has the trolley moved from the time the child begins to run?