Elevator Crashes

Huge debate at lunch today about how to save your life in case you are in an elevator crashing towards the ground. So the question was:

If you are in an elevator and it starts falling (the brakes fail or whatever), then can you save yourself from dying by jumping up at the exact moment the elevator hits the ground?

Or what if you hung onto something..like a rail on the roof..would that break your fall enough to save your life?

If yes, why
If no, why