Person's Distance from Shore After Moving 3m: Momentum & Center of Mass

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SUMMARY

The discussion centers on calculating the distance a 50 kg person is from shore after walking 3 meters on a 75 kg boat. Initially, the person is 6 meters from shore, and upon moving, the boat shifts left due to the conservation of momentum and the fixed center of mass of the system. The final distance from shore is determined to be 4.2 meters. The key takeaway is that as the person moves, the boat moves in the opposite direction, affecting the overall distance from the shore.

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A 50 kg person at the left end of a 75kg boat is 6 m from shore. The person walks to the other end of the boat 3m away. How far is the person from the shore now? The system center of mass fixed in space so as the person moves right, the boat moves left.

I know that the person moves 3 m to the right but how do I know how much the boat moves to the left? The answer is that the person will end up 4.2 m from shore, but how do I get there. If the person starts at 6 meter away and walks three meters towards the direction of the shore, the boat must travels a smaller distance relative to the person. This unit we're doing is on momentum and center of mass. I don't see how momentum will affect the result here, but maybe I am wrong. However, how does center of mass come into play here?
 
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take into account that weight has an affect on momentum (p = mv). I have no clue how center of mass comes to play since they don't provide any velocity. hmmm maybe the displacement you calculated is where the center of mass is? wait for other posters to confirm this
 
Simply use the fact that momentum is conserved, which will give you a relation between the person's and the boat's velocity, and displacement.
 

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