Two balls in free space are colliding with each other. Which of the following statements regarding linear momentum conservation of the system is true?

$A$ bomb initially at rest explodes by itself into three equal mass fragments. The velocities of two fragments are $(1\hat{i}+3\hat{j}) \ m/s$ and $(2\hat{i}-4\hat{j}) \ m/s$. The velocity of the third fragment (in $m/s$) is

$A$ bomb is projected upwards. At its topmost point,it explodes into three identical fragments. The first fragment reaches the ground in $10 \ s$,and the other two reach the ground in $20 \ s$ each. Find the maximum height $h$ reached by the original bomb. (in $m$)

$A$ jet engine works on the principle of

$A$ spacecraft of mass $M$ is moving with a velocity $V$. It suddenly breaks into two parts. One part of mass $m$ comes to rest. What will be the velocity of the other part?

An object of mass $2m$ is projected with a speed of $100 \ m/s$ at an angle $\theta = \sin^{-1}(3/5)$ to the horizontal. At the highest point,the object breaks into two pieces of same mass $m$ and the first one comes to rest. The distance between the point of projection and the point of landing of the second piece (in metres) is $(g = 10 \ m/s^2)$.