$A$ jet engine works on the principle of

$A$ 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?

An explosion breaks a rock into three parts in a horizontal plane. Two of them go off at right angles to each other. The first part of mass $1 \, kg$ moves with a speed of $12 \, m s^{-1}$ and the second part of mass $2 \, kg$ moves with $8 \, m s^{-1}$ speed. If the third part flies off with $4 \, m s^{-1}$ speed,then its mass is ......... $kg$.

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

$A$ body at rest breaks into three fragments. Two fragments of equal mass fly off perpendicular to each other with a speed of $30 \; m/s$. The mass of the third fragment is three times that of the other two fragments. What will be the direction and magnitude of the velocity of the third fragment immediately after the explosion?

$A$ 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 ............... $\, m/s$.