The entire mass of a system is assumed to be concentrated at a point, which we call the…

The entire mass of a system is assumed to be concentrated at a point, which we call the centre of mass. Such an assumption must be in someway helpful to us. This point may even be outside of the system. Once the journey has started, a given system may have exploded by itself or have broken down into number of pieces, each piece moving with a different velocity in a different direction than that of the original system, but this point of centre of mass will continue to move with same velocity in the same direction, as if nothing has happened.
Suppose a man of mass 60 kg is on a trolley of mass 40 kg moving at a speed of 4 m/sec. The man jumps off the trolley in the direction opposite to the motion of the trolley with a speed of 2 m/sec.
What may be essential condition to work out the velocity and direction of centre of mass :