$A$ body at rest explodes into two pieces of unequal mass. The parts will move

At a certain height,a body at rest explodes into two equal fragments with one fragment receiving a horizontal velocity of $10\sqrt{3} \text{ m/s}$. The horizontal distance between the two fragments,when their displacement vectors are inclined at $60^{\circ}$ relative to each other,is (take $g = 10 \text{ m/s}^2$):

$A$ gun fires a bullet of mass $50 \ g$ with a velocity of $30 \ m \ s^{-1}$. Due to this,the gun recoils with a velocity of $1 \ m \ s^{-1}$. What is the mass of the gun in $kg$?

$A$ bullet of mass $10\, g$ is fired from a gun of mass $1\, kg$. If the recoil velocity of the gun is $5\, m/s$,the muzzle velocity of the bullet is ........ $m/s$.

$A$ projectile of mass $3m$ is moving at $40\, m/s$ at its highest point,where it breaks into two parts $m$ and $2m$. Mass $2m$ moves vertically up at $25\, m/s$. The other part will move at a speed of .................... $m/s$.

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?