Physics mysteries

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18/09/2021

Jaroslav Kores, Ph.D.

Hypothetical rescue in a falling elevator

Can I save myself in a falling elevator by jumping just before impact?

I hope that no one will have to experience this situation because it will not be possible to jump in a falling elevator — I will explain the situation where we do not take into account the air resistance. If an elevator falls, the elevator will move with the acceleration of gravity g (we won’t count air resistance). When the elevator stops, the gravity of the Earth causes our body to fall down by accelerating with gravity, but the elevator floor prevents us from doing so. We feel solid ground under our feet. When we relax the muscles in our legs, our body will go down due to gravity and our legs will still remain on the floor. The moment the elevator breaks, it starts to fall with the same acceleration that we fall with. So if we relax the muscles in our legs, our body will fall down with an acceleration of g, but with the same acceleration that the floor of the elevator is moving below us. So we stay hanging over the floor with our legs bent. Only when the cabin stops will our feet reach the floor, but then it’s too late.

In reality, the car will be slowed down by air resistance, so its acceleration will be less than g, so our bent legs will allow our body to fall down a little faster than the speed of the elevator so we will be able to crouch. However it will take longer than if the cabin were standing still. If we were falling from the 10th floor (height 30 m), the elevator speed would be 88 km/h and I estimate the jump speed to be about 15 km/h. Our jump would reduce the speed to 73 km/h, which is not much anyway. In addition, it would be quite difficult to estimate exactly when to jump (in this case, we will fall in 2.5 seconds). Therefore, I would not rely on this possibility and if you are afraid of similar accidents, you better go on foot :).