$A$ 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 $ms^{-1}$ )

An isolated rail car of mass $M$ is moving along a straight,frictionless track at an initial speed $v_0$. The car is passing under a bridge when a crate filled with $N$ bowling balls,each of mass $m$,is dropped from the bridge into the bed of the rail car. The crate splits open and the bowling balls bounce around inside the rail car,but none of them fall out. Is the momentum of the rail car $+$ bowling balls system conserved in this collision?

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 .............. $\text{m/s}$.

$A$ spacecraft of mass $M$ is moving with a velocity $V$. It suddenly breaks into two parts. One part of mass $m$ comes to rest. What will be the velocity of the other part?

$A$ man of mass $m_1$ is standing on a platform of mass $m_2$ kept on a smooth horizontal surface. If the man starts moving on the platform with a velocity $v$ relative to the platform,then the recoil velocity of the platform is:

$A$ bomb of mass $16 \,kg$ explodes into two pieces of masses $4 \,kg$ and $12 \,kg$. The velocity of the $12 \,kg$ mass is $4 \,ms^{-1}$. The kinetic energy of the second piece (the $4 \,kg$ piece) is: (in $\,J$)