If a bomb is thrown at a certain angle with the horizontal and after exploding on the way the different fragments move in different directions,then the centre of mass

Two particles of the same mass are moving towards each other with velocities $2v$ and $v$ respectively. The velocity of the centre of mass of the system is:

The figure shows the positions and velocities of two particles. If the particles move under their mutual attraction,then the position of the centre of mass at $t = 1\,s$ is

Two persons of masses $55\, kg$ and $65\, kg$ respectively,are at the opposite ends of a boat. The length of the boat is $3.0\, m$ and it weighs $100\, kg$. The $55\, kg$ man walks up to the $65\, kg$ man and sits with him. If the boat is in still water,the center of mass of the system shifts by ....... $m$.

Two particles $A$ and $B$ initially at rest move towards each other under a mutual force of attraction. At the instant when the velocity of $A$ is $v$ and that of $B$ is $2v$,the velocity of the centre of mass of the system is:

$A$ body of mass $2 \,kg$ is moving towards north with a velocity of $20 \,m \,s^{-1}$ and another body of mass $3 \,kg$ is moving towards east with a velocity of $10 \,m \,s^{-1}$. The magnitude of the velocity of the centre of mass of the system of the two bodies is