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

$A$ bomb of mass $30 \, kg$ at rest explodes into two pieces of masses $18 \, kg$ and $12 \, kg$. The velocity of the $18 \, kg$ mass is $6 \, m/s$. The kinetic energy of the other mass is ....... $J$.

$A$ block of mass $m$ is moving with a velocity $u$ on a smooth horizontal surface towards a wedge of same mass $m$ initially kept at rest. The wedge is free to move in any direction. Initially, the block moves up the smooth inclined plane of the wedge to a height $h$ and then moves down back to the horizontal plane. In this process, the wedge gains a velocity equal to:

$A$ bomb is projected with $200\,m/s$ at an angle $60^o$ with the horizontal. At the highest point,it explodes into three particles of equal masses. One goes vertically upward with a velocity of $100\,m/s$,and the second particle goes vertically downward with the same velocity as the first. What is the velocity of the third particle?

$A$ man is standing at the centre of a frictionless pond of ice. How can he get himself to the shore?

$A$ particle of mass $5m$ at rest suddenly breaks on its own into three fragments. Two fragments of mass $m$ each move along mutually perpendicular directions with speed $v$ each. The energy released during the process is