From a stationary tank of mass $125000 \ lb$,a small shell of mass $25 \ lb$ is fired with a muzzle velocity of $1000 \ ft/sec$. The tank recoils with a velocity of ............ $ft/sec$.

$A$ particle of mass $m$ travelling along the $x$-axis with speed $v_0$ shoots out $1/3$ of its mass with a speed $2v_0$ along the $y$-axis. The velocity of the remaining piece is:

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

$A$ spacecraft of mass $M$ moves with velocity $V$ in free space at first,then it explodes breaking into two pieces. If after explosion a piece of mass $m$ comes to rest,the other piece of spacecraft will have a velocity

$A$ person of mass $M=90 \ kg$ standing on a smooth horizontal plane of ice throws a body of mass $m=10 \ kg$ horizontally on the same surface. If the distance between the person and the body after $10 \ s$ is $10 \ m$,then the kinetic energy $(KE)$ of the person (in $J$) is: (in $J$)

An object of mass $3\,m$ at rest splits into three equal fragments. Two fragments have velocities $v\hat j$ and $v\hat i$. The velocity of the third fragment is