Person in a boat. John (80 kg) is standing in a \(200 \mathrm{~kg}\) boat. He starts at one end and walks \(6 \mathrm{~m}\) to the other end of the boat. You may neglect drag forces between the boat and the water. (a) How far does the boat move in this process?

The center of mass is a crucial concept when dealing with systems of particles or objects. It represents the average location of the mass of the system. For John and the boat system, the center of mass acts as if all the mass of the system is concentrated at one point.
In our exercise, no external forces are acting on John and the boat. Therefore, the center of mass of the system must remain in the same place throughout John's walk.
This is because the internal movements do not impact the total momentum of the system.
The position of the center of mass is maintained, thus the displacement of John and the boat must balance each other out.

Displacement refers to the change in position of an object. It is a vector quantity, meaning it has both magnitude and direction.
In the problem, John walks 6 meters from one end of the boat to the other. However, because the boat is free to move, the boat itself displaces in response to John's movement to keep the center of mass constant.
The total displacement of the system (John plus boat) must account for both John’s movement and the boat's counter-movement.
In our solution, by using the conservation of momentum and setting up the equation, we find that the boat moves approximately 1.714 meters in the opposite direction of John's walk to ensure that the center of mass of the system remains unchanged.

External forces are forces that act on a system from outside the system's boundaries. Examples include gravitational forces, friction, and applied forces.
In our exercise, we assume there are no external forces acting on John and the boat. This assumption simplifies our calculations and refers to the conservation of momentum principle.
When no external forces act on the system, the total momentum of the system before and after an event must be the same.
Because John's walking is an internal movement within the system and there are no external forces like friction from water (neglected in the problem), the momentum of the John-boat system is conserved, allowing us to calculate the boat's displacement accurately.