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The boat will keep moving
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because there's no force on the boat; it's going to keep moving.
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The question is, "How come I suddenly have momentum in my system
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when I had no momentum before?"
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It's because the F external has now come into play.
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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