The physics of a jump?

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Hello there!

I was thinking about jumping the other day. How would one explain jumping by physics.

So, before you jump, you always bend your knees. This knee bending, from my point of view shouldn't be analogized with the build up elastic energy, since the force that will cause the jump will come from outside of the observing system :) (from the contractions of our muscles).

Therefor, the crouching serves only to provide the path on which a force of our muscles cad do work on.

So now, lets say we're starting to jump (from the crouched position). We're starting to exert a force on the ground which replays back with the same force which is larger that the force that it generally exerts do to our weight.

So since that force is larger that the force of gravity, it is that force that actually gives us a push up. So if you concentrate on this fact while you jump, you can actually feel the ground pushing you.

So now, does the impulse of force has any effect on how high we jump (if in the end the integral of force and path equal always the same work) ?
 

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So now, does the impulse of force has any effect on how high we jump (if in the end the integral of force and path equal always the same work) ?
If the impulse is the same but the time of the jump is shorter the pushing force will be greater and so will the work.
 

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