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So I recently worked out a problem in my mechanics class about two people jumping off a frictionless railroad cart at speed u. The result is that the cart will move faster if they each jump off separately than it would have if they both jumped at the same time.

I've been trying to understand intuitively why this is so, but I actually reach the opposite conclusion. My explanation is that when one person jumps they exert force f. So when they jump together 2f is exerted on the cart. When they jump separately f is exerted twice, but the first time its exerted is on a heavier cart (because cart plus the mass of the person still on) so it will accelerate to a slower speed. This implies the opposite of the actual result.