I've always been under the impression that jumping in an elevator wouldn't help at all, especially after reading a snippet of physics where Einstein said that free fall was identical to zero gravity.
I just watched an episode of QI (a British game show) where they said that jumping would only take off about five pounds of force... How would jumping help at all? If the elevator is in free fall, then you're not really jumping--you're just pushing, right?
Yep. You're pushing. In fact, with one jump, you will rocket straight up and probably bash your head agaist the ceiling. By the equivalence principle, the freefalling elevator is equal to an inertial box in space. If you jump in the box, you will push it "downwards" (meaning away from your feet--space has no up), and you will go "upwards", by momentum conservation. The net effect will be that you will zoom towards the ceiling.
I don't see what they mean with "jumping takes off 5 pounds of force". In freefall, the minute you jump you lose contact with the floor--so there is no force in the inertial system whatsoever immediately after you jump.
Always eager to do original research I have watched QI Series 5 Episode 7 "Espionage", and the question was "what is the best thing to do in a falling lift?".
Steven Fry mentioned that there was a theory that you should jump just before the lift hits the ground, though he pointed out that this would reduce the relative velocity between you and the ground by only about 5 miles per hour, and since a lift freely falling the length of the Empire State building would reach 120mph, this would do little to save you.
As an aside, he also pointed out that the lift will bounce when it hits the bottom, so even if you jump just before impact you will meet the lift floor travelling upwards at somewhere between 115 and 235mph (depending on the co-efficient of restitution), suggesting once again that jumping isn't a terribly effective strategy.
The (allegedly) correct answer is to try and get someone, preferably someone with a higher than average inertial mass, between you and the floor to cushion your impact.
Anyhow - to the physics: if you and the lift are falling together then jumping will indeed reduce your velocity with respect to the floor. If you consider the freely falling reference frame, when you jump you are pushing yourself up and pushing the lift down, so your velocity wrt the ground decreases and the velocity of the lift wrt the ground increases.
You ask "then you're not really jumping--you're just pushing, right?", and presumably you're thinking that because you and the lift are in free fall the lift will just move away from you. This is quite correct, but I would guess a lift is a lot heavier than you are, so when you jump you will move a lot faster than the lift will. You wouldn't be able to jump as effectively as you could standing on the ground, but you could probably jump reasonably hard. This may give you some satisfaction in the few milliseconds before the ground terminates your career as an experimental physicist.
