$A$ man weighing $80 \, kg$ is standing in a trolley weighing $320 \, kg$. The trolley is resting on frictionless horizontal rails. If the man starts walking on the trolley with a speed of $1 \, m/s$ relative to the trolley,then after $4 \, s$ his displacement relative to the ground will be ........ $m$.

In an explosion,a body breaks up into two pieces of unequal masses. In this process:

$A$ bomb of mass $9 \text{ kg}$ explodes into two pieces of mass $3 \text{ kg}$ and $6 \text{ kg}$. The velocity of mass $3 \text{ kg}$ is $16 \text{ m/s}$. The kinetic energy of mass $6 \text{ kg}$ (in joule) is

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

$A$ girl riding a bicycle along a straight road with a speed of $5 \, m/s$ throws a stone of mass $0.5 \, kg$ which has a speed of $15 \, m/s$ with respect to the ground along her direction of motion. The mass of the girl and bicycle is $50 \, kg$. Does the speed of the bicycle change after the stone is thrown? What is the change in speed,if so?

$A$ man of mass $m_1$ is standing at a height $h$ from the floor in a gravity-free room. He throws a ball of mass $m_2$ downwards with a speed $u$. Find the distance of the man from the floor when the ball reaches the floor.