Physics of Elevator: Will Inertia Allow a Person to Touch the Roof?

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frankenkash
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This, in my opinion, is a no-brainer. But i decided to post this as a confirmatory proof to a friend who refuses to see reason!

The argument: In an elevator whose cable has snapped, irrelevant of whether it's stationary or going up/down, the person inside will travel upwards in the falling lift to hit the roof. Now i hope i have not changed the context of this question or changed how it was stated, but I would like to ask- WILL A PERSON IN A FALLING ELEVATOR EVER TOUCH THE ROOF (without jumping/external force) DUE TO INERTIA OR ANY OTHER SUCH FORCE? Or would he just feel weightless from the second the cable snaps to the time the thing touches bottom... (lets not bring in practical forces such as wind resistance etc etc)
 
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If you're in an elevator and the cable snaps so that you and the elevator are in free fall, then you'll feel weightless. You won't magically fly up to the ceiling. (Of course real elevators have emergency brakes.)
 
You were pushing against the floor with your legs, before the cable snapped, and you will get some upwards velocity (relative to te elevator), since you can't stop pushing immediately.
Of course you'll lose contact with the floor very quickly, so you won't get a lot of velocity.