There have been quite a few plane crashes the past week and this question popped into my head of which I need a good explanation in science about the possibility of survival or not and why.

Assuming I am on a plane that is quickly losing altitude, just before the plane hits the ground I jump off the plane.

  1. Is it even possible to jump?
  2. If I can jump, will the gravitational pull be different and thus make me survive? Would this be equal to jumping off the ground? (Assume that I am immune to the plane explosion)

You can't jump very quickly. The average vertical jump of NBA players is 28 inches. How fast are they going at max?

$$v^2 = 2 a x$$ $$v = \sqrt{2 g (0.71m)}$$ $$ v = \sqrt{13.95m^2/s^2}$$ $$ v = 3.7 m/s$$

That's not very fast. It means that at a maximum you can remove less than 4m/s of your impact speed. Since a plane crash may be 100m/s, that doesn't help much.

  • $\begingroup$ In addition, jumping would be more difficult since the plane's floor isn't providing a support force - it's in freefall too. It would feel more like kicking off a wall swimming than jumping off the ground. $\endgroup$ – Señor O Jul 24 '14 at 16:55
  • $\begingroup$ Perhaps a young grasshopper could well pull this off. $\endgroup$ – Andres Salas Jul 24 '14 at 17:18
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    $\begingroup$ More simply: the NBA jumper would be able to compensate for the velocity gained by a 28 inch free-fall... $\endgroup$ – DJohnM Jul 24 '14 at 21:58

You cannot jump from an object in free fall. The reason is this:

If you are standing on an object in free fall this means you are yourself in free fall. In that case the Normal force experienced by you is $0$ N. If the Normal force is $0$ N then you cannot exert a force on the object (hence the object cannot exert a force on you via Newtons 3rd Law) therefore you cannot jump and avoid the crash.

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    $\begingroup$ I have to say I don't think that's true. Even in free fall I can produce a force between me and the plane by straightening my legs, and that will change my velocity (and the velocity of the plane). $\endgroup$ – John Rennie Jul 24 '14 at 16:17
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    $\begingroup$ @JohnRennie I believe since there is a normal force acting on you (initially that normal force would cancel gravity, until the object loses contact with you) you wouldn't be able to do that would you? $\endgroup$ – Constandinos Damalas Jul 24 '14 at 16:26
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    $\begingroup$ If I grab hold of the seat arms and use them to pull myself into a crouch I can then jump away from whatever my feet are in contact with. It's certainly true that without something to hold I wouldn't be able to crouch down on the floor. $\endgroup$ – John Rennie Jul 24 '14 at 16:37

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