Why can't you jump in a falling elevator?

If the elevator cable broke, why couldn't you jump right before the elevator hits the ground and not be hurt?

Or are you? Remember, when you jump that one centimeter, that is one centimeter relative to the floor of the elevator! The elevator is still falling, and so are you! Imagine the elevator floor is glass, and you can see the ground rushing up at you. That one centimeter jump doesn't look like it'll help much now, does it? All you've really done is add another centimeter to the length of your fall. Your body will impact at the same speed, only a fraction of a second later.

Now if you are trying to negate the speed of your fall by jumping upwards, that won't work well either. In free fall, you fall 10 meters in the first second, 20 in the next second (for a total of 30 meters), 30 the next (total of 60) and so on, falling 10 meters per second faster for every second of the drop. [Oops!(August 11, 1999): I made a small error here. You fall 5 meters the first second, not 10. By the end of the first second, you're falling at 10 meters per second, but you have only fallen 5 meters. At the end of the second second you have fallen 20 meters, and at the end of the third you'll have dropped 45 meters. The distance in meters goes as 5 x time^2]. Now, friction and air resistance will eventually stop the downward acceleration. A human freely falling tends to peak at about 180 kilometers per hour, or about 50 meters a second. That's fast, about twice as fast as a car on a highway. An elevator might do more in a big high rise. Now try jumping that fast! I am guessing that the most you can jump straight up is a meter or two per second.

Think of it this way. Instead of jumping up, think about how hard it is when you hit the ground after jumping down off a wall. This is the same problem as the elevator, but in reverse. After jumping even a couple of meters your knees hurt, right? Now imagine falling 20 meters! Ouch!