Center of Mass Questions

A man of $50\text{ kg}$ mass is standing in a gravity free space at a height of $10\text{ m}$ above the floor. He throws a stone of $0.5\text{ kg}$ mass downwards with a speed $2\text{ m/s}$. When the stone reaches the floor, the distance of the man above the floor will be:

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:

Three masses are placed on the x-axis: $300\text{g}$ at origin, $500\text{g}$ at $x=40\text{cm}$ and $400\text{g}$ at $x=70\text{cm}$. The distance of the centre of mass from the origin is:

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