In the scenario of a boat with two men at opposite ends, the center of mass (COM) remains stationary due to the absence of external forces. When the men move towards the center, the boat shifts by 2/15 m towards the left, despite the initial doubt about movement without external forces. The differing weights of the men create an initial imbalance, causing the boat to move, as the men push against it when they walk. The discussion highlights that while the boat's movement may be minimal and not easily perceptible, it is a result of the conservation of momentum within the closed system of the boat and men. Ultimately, the boat's motion is a consequence of the internal dynamics of the system rather than external influences.