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Previously, it was just you and the boat
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and you couldn't change your total momentum.
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But the ground is now pushing you,
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and it's obviously pushing you to the right
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because you were flying to the left and you were stopped.
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So, your combined system, you and the boat,
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have a rightward force
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acting for the time it took to stop you;
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it's that momentum that's carried by the boat.
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A better way to say this is, you and the boat exchange momenta,
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you push the boat to the right, you move to the left,
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and your momentum is killed by the shore.