Will jumping just before an elevator crashes save you? Probably not. Even if someone managed to jump at the last second, they would still be moving downward at almost the same speed, so the change in the impact would be tiny. The real danger in a crash is not just “speed,” but how quickly that speed has to drop to zero. If the stopping distance is very short, the deceleration is enormous, and the body takes the force.
A simple way to picture this is to turn the elevator sideways and imagine it as a train. If a train slams into a cliff, running toward the back of the train does not cancel the crash. To cancel the forward motion, the runner would need to sprint at roughly the same speed as the train, which is far beyond human ability. The same idea works with a bus: if a bus is coming at 60 km/h, running away might reduce the closing speed a little, but it would not turn a deadly collision into a safe one.
Elevators have a lot of safety features. They have automatic brakes that deploy when cables snap or when the power goes. If those failed, there is friction with the side of the elevator shaft, and there is also a lot of air resistance because the elevator shaft is not wide enough to let the air disperse. The likelihood of an elevator plunging all the way down the shaft without being slowed down is incredibly slim, but, for the sake of this question, let’s assume it happened and you are in a 20 story building.
The height of each story varies depending on the architect, but let’s assume a 20 story building is 80 meters. Also, for the sake of argument, let’s assume no friction and no air resistance. To calculate the speed of the elevator car at impact we need to know the distance it falls and gravity. The equation is velocity squared equals two times gravity times the distance fallen. (v2=2gh) So, gravity is 9.81 m/s2 and we are at 80 m, so 2 x 9.81 x 80 = 1569.6. We need to get the square root of that to get the velocity, which gives us 39.6 m/s, or 143 km/h. To negate that impact, you would need to jump at a vertical speed of 143 km/h, which is impossible for a human to do. Olympic high jumpers, who are arguably some of the best jumpers in the world, attain jump speeds of 4.8 m/s, which is 17.28 km/h. So, a professional high jumper could reduce the impact with the ground from 143 km/h to 126 km/h, which is still fatal.
It is also helpful to think in terms of momentum and energy. Momentum is mass times velocity, so if the velocity is still huge, the momentum is still huge. Kinetic energy scales with the square of velocity, so shaving a little speed off the top does not remove much of the danger. And if the elevator floor stops over only a few centimeters, the body has to stop in the same short distance. A small reduction in speed does not change that basic problem.
We can think about this with our bus again. Imagine the bus is travelling at 143 km/h, and Usain Bolt steps in front of it. He immediately turns and reaches his top speed, 36 km/h, before the bus hits him. He will reduce the impact but not by enough to make any difference.
There are three other things we need to consider as well. The first is timing. To make this work, you would need to jump before the elevator car hit the ground, not as it hit the ground. You cannot see out of the elevator to time the jump, but let’s assume that you are in a transparent elevator. It takes a human about 0.2 seconds to react, and then another half second to perform the mechanics needed to jump: extending the legs and pushing off. The elevator car will take 4.04 seconds to make the fall, so you need to begin the jump 0.7 seconds before impact, which is at a height of 2.4 m above the ground. If you could judge that, then you could theoretically make the jump in time.
The second issue is space. In the last 0.7 seconds, a jump takeoff speed of 4–5 m/s would carry the body upward by several meters relative to the car. Elevator cabins are not tall enough for that, so a strong jump would likely end with the jumper hitting the ceiling before the crash. That ceiling impact would not be the main danger compared to the crash itself, but it would ruin posture and timing and could cause injury before the main impact. Even if you can somehow jump vertically without impacting the roof, the elevator car is going to hit the floor with so much energy that it will concertina and you will be squashed.
The third thing is that as the elevator falls down the shaft, you will be in free fall. In true free fall, the person becomes effectively weightless inside the car. Without body weight pressing feet into the floor, it becomes difficult to generate a strong jump at all. If there is no solid contact with the floor, there is no reliable way to create that upward takeoff speed in the first place.
The best advice for if you are ever in this situation is to lie on the floor of the elevator and spread yourself out as much as possible. This would spread out the impact force over a larger area, potentially helping you survive. Although, in free fall, you would not be able to get down to the floor, and the impact would probably still be fatal. That is why elevators have so many safety features. And this is what I learned today.
Sources
https://van.physics.illinois.edu/ask/listing/139
https://van.physics.illinois.edu/ask/listing/115
https://www.usab.com/news/2015/04/the-science-behind-your-vertical-leap
https://www.greatestsportingnation.com/content/high-jump-technique-0
Photo by cottonbro studio: https://www.pexels.com/photo/close-up-shot-of-a-hand-pressing-an-elevator-button-8453040/