Great question! How much you get hurt depends on the force on you when you hit the ground. Remember that force is proportional to the change in momentum and inversely proportional to the length of time over which the momentum changes.
Since momentum is mass times velocity, the faster you’re going when you hit the ground, the more force you will feel, and the more it will hurt. If the elevator has been falling for a while, then it’s probably moving very fast. If you jump up, then you’ll change your velocity just a little bit. So you’ll be going a tiny bit slower when you hit the ground. So, technically speaking, you would probably not be hurt quite as much. But this difference would probably be so small as to not be noticeable. In particular, if you’re falling so fast as to be killed in the fall, jumping would most likely not make enough of a difference to save your life.
p.s. If you’re like me, you might at first think that jumping up won’t do any good because you’ll just fall back down, speeding up again. In fact, Tamara is right. Once the elevator is falling more than half as fast as the speed you get by jumping from rest, jumping reduces your energy, and will soften the fall. If you tried jumping just as soon as the elevator started to fall, you’d actually end up falling from a greater height, and hit harder. The best time to jump is right before landing. If you jump too early, you’ll just crash your head into the ceiling of the elevator, and get all of your original momentum back.
To anyone who might have read this during the days when I had posted an ’improved’ but wrong answer, I apologize.
(As a practical problem, jumping might not be a good idea because then you hit a fixed elevator floor, rather than having you and the elevator crash together into the shaft bottom, maybe with a more stretched-out collision.) Mike W.
(published on 10/22/2007)