The woman A, the captain B, and the sailor C weigh 120,180, and 160 lb, respectively, and are si

step 1 So here on this problem we are given that the weight of the woman is 120 pound so weight of this

The woman A, the captain B, and the sailor C weigh 120,180,...

The woman $A$, the captain $B$, and the sailor $C$ weigh $120,180,$ and $160 \mathrm{lb},$ respectively, and are sitting in the 300 -lb skiff, which is gliding through the water with a speed of 1 knot. If the three people change their positions as shown in the second figure, find the distance $x$ from the skiff to the position where it would have been if the people had not moved. Neglect any resistance to motion afforded by the water. Does the sequence or timing of the change in positions affect the final result?

Key Concepts

Center of Mass

The center of mass is the weighted average position of all mass in a system. Its location determines how the total mass of an object or system will behave under motion. When no external forces act on the system, the center of mass does not change its state of motion regardless of internal movements. In this problem, the skiff and people constitute a closed system where the center of mass remains constant even as the individuals move around on the skiff.

Conservation of Momentum

Conservation of Momentum is a fundamental principle stating that in the absence of external forces, the total momentum of a system remains constant over time. When people move relative to the skiff, they create internal forces; however, these forces cancel out and do not change the overall momentum of the system. Thus, the skiff’s resulting displacement is entirely determined by the requirement that the center of mass remains unchanged.

Internal Forces and Relative Motion

Internal forces are forces that the parts of a system exert on each other, and they do not affect the net external motion of the system's center of mass. Relative motion refers to the movement of objects within the system relative to one another. In scenarios like this, where individuals change their positions, the sequence or timing of their moves is irrelevant to the final outcome because only the initial and final configurations of the mass distribution impact the displacement of the skiff.

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