Jokes2 mins ago
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When you push off from the falling lift, an equal and opposite force would apply to the mass of the lift, (cables and counterweight disconnected). This mass may be about a tonne, so they would increase velocity at a tenth of your jumping speed.
As for your jumping speed, it might be enough to raise your centre of gravity by half a metre tops, meaning you would reduce your impact by about 3 metres per second (8mph). The falling lift cabin accelerates by about 10 metres per second for every second of freefall, so your effort would be almost futile for any big drop. Besides, if you jumped just a fraction too soon you would brain yourself on the ceiling in freefall an instant before being crushed on the deck.
Your best bet would be to lie flat on the floor if you could and let the crumple zones in the bottom of the shaft to the deforming instead of you!
Mythbusters on the Discovery Channel tried out this myth in episode 17. http://dsc.discovery.com/fansites/mythbusters/episode/episode_03.html
It would also depend on whether the lift was an open top as you may be able to jump at the split second it crashes but the ceiling would then come down and squish you flat.