At high altitude,a body at rest explodes into two equal fragments,with one fragment receiving a horizontal velocity of $10 \, m/s$. The time taken by the two radius vectors connecting the point of explosion to the fragments to make an angle of $90^o$ is ............ $s$.

$A$ bomb of mass $60 \ kg$ is at rest. It explodes into two fragments. The kinetic energy of the $40 \ kg$ fragment is $96 \ J$. What is the kinetic energy of the other fragment in $J$?

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?

$A$ man of mass $m_1$ is standing on a platform of mass $m_2$ kept on a smooth horizontal surface. If the man starts moving on the platform with a velocity $v$ relative to the platform,then the recoil velocity of the platform is:

$A$ bomb of mass $9 \ kg$ explodes into two pieces of masses $3 \ kg$ and $6 \ kg$. The velocity of mass $3 \ kg$ is $16 \ m/s$. The $KE$ of mass $6 \ kg$ is ............ $J$.

$A$ $300 \ kg$ trolley carrying a $25 \ kg$ sandbag is moving on a frictionless track with a uniform speed of $27 \ km/hr$. After some time,sand starts leaking out of the bag at a rate of $0.05 \ kg/s$ and falls onto the floor of the trolley. Find the speed of the trolley in $km/hr$ when the sandbag is completely empty.