$A$ wagon weighing $1000\, kg$ is moving with a velocity of $50\, km/h$ on smooth horizontal rails. $A$ mass of $250\, kg$ is dropped into it. The velocity with which it moves now is ......... $km/h$.

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. What is the average speed of the rail car $+$ bowling balls system some time after the collision?

$A$ bullet of mass $50 \, g$ is fired from a $5 \, kg$ gun with a velocity of $1 \, km/s$. The speed of recoil of the gun is .......... $m/s$.

$A$ body of mass $M$ at rest explodes into three pieces,in the ratio of masses $1: 1: 2$. Two smaller pieces fly off perpendicular to each other with velocities of $30 \, m/s$ and $40 \, m/s$ respectively. The velocity of the third piece will be ............... $\, m/s$.

Three particles of masses $10\;g, 20\;g$ and $40\;g$ are moving with velocities $10\hat{i}, 10\hat{j}$ and $10\hat{k}\;m/s$ respectively. If due to some mutual interaction,the first particle comes to rest and the velocity of the second particle becomes $(3\hat{i} + 4\hat{j})\;m/s$,then the velocity of the third particle is

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