URGENT ! a child is standing at one end of a long trolley moving with a speed v on a smooth horizontal track . if the child starts running towards the other end of the trolley with a speed u , then the centre of mass of the system ( trolley + child) will move with a speed ???
When the child is standing on the trolley, both child and trolley are moving with the same velocity = v
So, their centre of mass is also moving with the velocity of the vehicle,
vcom = mv + Mv / (m + M) = v
the velocity of centre of mass changes only if the system is subjected to net external force. But since the only forces involved in the child + trolley system are internal(action-reaction pair) when the child runs on the trolley. Therefore, the velocity of their centre of mass will remain unchanged. It will be v