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Why do basketball players bend their knees when landing after a jump?

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Answer: It lets muscles absorb energy over a longer stopping motion

It lets muscles absorb energy over a longer stopping motion ✓ — Bending the knees, with motion at the hips and ankles, gives muscles distance and time to absorb landing energy. For the same change in momentum a longer stopping time lowers average net force, although peak loads also depend on the landing pattern.

It stores all impact energy in the knee bones for later — Bones do not store all landing energy like a battery. Muscles absorb much of it as they resist joint bending, while tendons can temporarily store and return some elastic energy.

It prevents any change in the body’s downward momentum — The body must lose its downward momentum to stop falling. Bending the legs changes how that momentum is brought to zero, not whether it changes.

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