$A$ body,whose momentum is constant,must have constant

$A$ 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.

Neglecting friction,if a person sitting at the back of a motorcycle moving on a straight path falls off while the motorcycle is in motion,will the velocity of the motorcycle increase or decrease? Why?

$A$ ball of mass $200\,g$ rests on a vertical post of height $20\,m$. $A$ bullet of mass $10\,g$,travelling in a horizontal direction,hits the centre of the ball. After the collision,both travel independently. The ball hits the ground at a distance of $30\,m$ and the bullet at a distance of $120\,m$ from the foot of the post. The value of the initial velocity of the bullet will be $............m/s$ (if $g = 10\,m/s^2$).

An explosion breaks a rock into three parts in a horizontal plane. Two of them go off at right angles to each other. The first part of mass $1 \, kg$ moves with a speed of $12 \, m s^{-1}$ and the second part of mass $2 \, kg$ moves with $8 \, m s^{-1}$ speed. If the third part flies off with $4 \, m s^{-1}$ speed,then its mass is ......... $kg$.

$A$ spacecraft of mass $M$ moves with velocity $V$ in free space. It explodes and breaks into two pieces. If after the explosion,a piece of mass $m$ comes to rest,what will be the velocity of the other piece of the spacecraft?