$A$ person of mass $80 \ kg$ is standing on a trolley of mass $320 \ kg$. The trolley is at rest on a frictionless horizontal rail. If the person walks on the trolley at a speed of $1 \ m/s$,what will be their displacement relative to the ground after $4 \ s$?

$A$ bomb of mass $1 \,kg$ initially at rest,explodes and breaks into three fragments of masses in the ratio $1: 1: 3$. The two pieces of equal mass fly off perpendicular to each other with a speed $15 \,m / s$ each. The speed of the heavier fragment is ........... $m / s$.

$A$ 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 .............. $J$.

$A$ particle of mass $4m$ explodes into three pieces of masses $m, m$ and $2m$. The equal masses move along the $X$-axis and $Y$-axis with velocities $4 \text{ ms}^{-1}$ and $6 \text{ ms}^{-1}$ respectively. The magnitude of the velocity of the heavier mass is

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

$10m$ is the total mass of a cannon that includes all shells. Initially, the cannon is moving with a velocity of $10 \ m/s$ along a horizontal frictionless path. If the cannon fires $n$ shells of mass $m$ in the direction of motion of the cannon one by one with velocity $u$ with respect to the ground, which of the following statements is correct? (Neglect any friction force)