A lot of these answers are focused on physics, and I guess that makes sense.
But the other reason jumping wouldn’t save your life, is because elevators are already designed not to kill you. Even if all the safety mechanisms – of which there are many – were to all fail at the same time, and all the cables were severed, in the bottom of the elevator shaft there are buffers that will decelerate the car from freefall to a stop, much more gently than just hitting the floor. You’d probably still be severely injured in such an event, but you probably won’t die.
So the real answer as to why jumping wouldn’t save your life, is because your life is already in quite good hands.
You can jump what, 3 feet? So you might get rid of 3 feet worth of energy from whatever height you started. 47 vs 50 feet fall doesn’t seem like much of a difference to me. Just delaying your death by a fraction of a second.
Even if jumping worked, you have no way of knowing when the elevator is about to hit the bottom, because you can’t see through the floor.
I think the best strategy for survival is to wedge yourself hard into a corner trying to get as much friction against the walls as possible, and spread your deceleration out over as much vertical distance as possible.
There a lot of answers that are correct here.
But let’s go back to some basic physics: potential and kinetic energy.
If you lift something up from the ground then it has potential energy. How much? Well let it go and see what happens. It will fall to the ground with a particular acceleration and a speed when it hits the ground. All of that potential energy got converted into kinetic energy.
Now let’s use this on the elevator.
When the elevator drops in free fall it converts potential energy to kinetic energy with maximum conversion when it hits the ground.
If you want to jump to counter that velocity then you have a very easy equation to solve.
**You need to do what the elevator has done but in reverse.**
*So you will need to jump so fast (kinetic energy) that you can reach the same point (potential energy) that the elevator first started to free fall.*
So the question is can you jump multiple floors up?
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