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

$A$ bomb at rest explodes into three parts of equal mass. If the momentum of two parts are $-2 p \hat{i}$ and $p \hat{j}$,find the magnitude of momentum of the third part.

$A$ particle of mass $4 M$ which is initially at rest explodes into three pieces of masses $M, M$ and $2 M$. The equal masses move along $X$ and $Y$-axes with velocities $4 \ m s^{-1}$ and $6 \ m s^{-1}$ respectively. The magnitude of the velocity of the heavier mass is

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

$A$ shell initially at rest explodes into two pieces of equal mass. Then the two pieces will:

$A$ $100\, g$ iron ball having velocity $10\, m/s$ collides with a wall at an angle of $30^\circ$ with the wall and rebounds with the same angle. If the period of contact between the ball and the wall is $0.1\, s$,then the force experienced by the wall is ........... $N$.