Newton's third law of motion leads to the law of conservation of

Two persons of mass $m_1$ and $m_2$ are standing at the two ends $A$ and $B$ respectively,of a trolley of mass $M$ as shown. When only the person standing at $B$ jumps from the trolley towards the right while the person at $A$ keeps standing,then

$A$ 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 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.

When two balls at the same temperature collide,which of the following quantities is conserved?

An artillery piece of mass $M_1$ fires a shell of mass $M_2$ horizontally. Instantaneously after the firing,the ratio of kinetic energy of the artillery and that of the shell is: