$A$ 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:

$A$ 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 $M$ moves with velocity $V$ in free space. It explodes and breaks into two pieces. If after the explosion,a piece of mass $m$ comes to rest,what will be the velocity of the other piece of the spacecraft?

$A$ person of mass $M=90 \ kg$ standing on a smooth horizontal plane of ice throws a body of mass $m=10 \ kg$ horizontally on the same surface. If the distance between the person and the body after $10 \ s$ is $10 \ m$,then the kinetic energy $(KE)$ of the person (in $J$) is: (in $J$)

$A$ girl riding a bicycle along a straight road with a speed of $5 \, m/s$ throws a stone of mass $0.5 \, kg$ which has a speed of $15 \, m/s$ with respect to the ground along her direction of motion. The mass of the girl and bicycle is $50 \, kg$. Does the speed of the bicycle change after the stone is thrown? What is the change in speed,if so?

$A$ body moving with speed $v$ in space explodes into two pieces of masses in the ratio $1 : 3$. If the smaller piece comes to rest,the speed of the other piece is