In a gravity-free space,a man of mass $M$ standing at a height $h$ above the floor,throws a ball of mass $m$ straight down with a speed $u$. When the ball reaches the floor,the distance of the man above the floor will be

$A$ 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 at rest explodes into three pieces of equal masses. If two pieces move perpendicular to each other,each with a speed $v$,then the speed of the third piece is:

$A$ bomb of mass $16 \ kg$ at rest explodes into two pieces of masses $4 \ kg$ and $12 \ kg.$ The velocity of the $12 \ kg$ mass is $4 \ m s^{-1}.$ The kinetic energy of the other mass is .............. $J$.

$A$ man fires a bullet of mass $200 \,g$ at a speed of $5 \,m/s$. The gun has a mass of $1 \,kg$. With what velocity does the gun recoil backwards?

$A$ 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