Can you jump off of a falling object before hitting the ground and save yourself?

Since you would already be falling down together with the object at the same speed as the object, jumping off the object would at best result in a minimally diminished impact velocity, assuming your jump involves an upward motion.
Considering that you have to save yourself means that the impact velocity would already be deadly and it would still be deadly even if you jumped off the object.
So no, all your bones would still be crushed by the impact, as would your inner organs, your skin would burst open in some places, with blood splattering out and your head would be split open like a watermelon with your brain splashing out like jelly.
And you would die, too, most certainly.

the mythbusters say no

Unless you’re strong enough to completely reverse the speed you’re falling at at that point, stopping in mid air before resuming the fall due to gravity, then no.

@Thammuz
And since that acceleration would be equal to the deceleration during impact, the jump itself would kill you anyway.

@ragingloli You’re forgetting that half of the energy would be directed to accelerating the object against which you’re pushing, and only half to your own deceleration, meaning that you’d require double the energy to counteract your downward acceleration.

@SmashTheState i don’t think it’s worth mentioning, afterall even without double the energy it’s impossible.

@ragingloli i didn’t think about that…

@SmashTheState Took the words right out of my mouth. Though more than likely it would just push the base down and not have much if any effect on you.

That’s what happens to the Earth when you jump. It’s pushed down. It just so happens that people on the other side of the planet are jumping too and pushing it right back up to your feet.