The figure shows a man of mass $m$ standing at the end $A$ of a trolley of mass $M$ placed at rest on a smooth horizontal surface. The man starts moving towards the end $B$ with a velocity $u_{rel}$ with respect to the trolley. The length of the trolley is $L$. When the man reaches the end $B$,the distance moved by the trolley with respect to ground is

$A$ shell fired from a gun at an angle to the horizontal explodes in mid-air. Then the centre of mass of the shell fragments will move

Two particles which are initially at rest,move towards each other under the action of their internal attraction. If their speeds are $v$ and $2v$ at any instant,then the speed of centre of mass of the system will be

Explain translational motion by the given illustration.

Given below are two statements: one is labelled as Assertion $(A)$ and the other is labelled as Reason $(R)$.
Assertion $(A)$: When a firecracker (rocket) explodes in mid-air,its fragments fly in such a way that the centre of mass of the fragments continues to move along the same parabolic path that the firecracker would have followed had it not exploded.
Reason $(R)$: The explosion of a firecracker (rocket) occurs due to internal forces only,and no external force acts to cause this explosion.