$A$ bomb moving with velocity $(40 \hat{i} + 50 \hat{j} - 25 \hat{k}) \text{ m/s}$ explodes into two pieces of mass ratio $1:4$. After the explosion,the smaller piece moves away with velocity $(200 \hat{i} + 70 \hat{j} + 15 \hat{k}) \text{ m/s}$. The velocity of the larger piece after the explosion is:

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 is fired from a gun. If the gun recoils freely,the kinetic energy of the gun will be

$A$ body,whose momentum is constant,must have constant

$A$ man of mass $100\,kg$ is standing on a platform of mass $200\,kg$ which is kept on a smooth ice surface. If the man starts moving on the platform with a speed $30\,m/s$ relative to the platform,then calculate with what velocity relative to the ice the platform will recoil.

$A$ 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 .................... $m/s$.