$A$ 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 of mass $1 \,kg$ initially at rest,explodes and breaks into three fragments of masses in the ratio $1: 1: 3$. The two pieces of equal mass fly off perpendicular to each other with a speed $15 \,m / s$ each. The speed of the heavier fragment is ........... $m / s$.

$A$ 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 ........ $m$.

$A$ bomb of mass $9 \text{ kg}$ explodes into two pieces of mass $3 \text{ kg}$ and $6 \text{ kg}$. The velocity of mass $3 \text{ kg}$ is $16 \text{ m/s}$. The kinetic energy of mass $6 \text{ kg}$ (in joule) is

$A$ $100\, g$ 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 ........... $N$.

Three masses $m$,$2m$,and $3m$ are moving in the $x-y$ plane with speeds $3u$,$2u$,and $u$ respectively,as shown in the figure. The three masses collide at the same point $P$ and stick together. The velocity of the resulting mass will be