Can a person free fall onto a big block of jelly and survive disregarding the eventual suffocation?

Question

Assuming the height is sufficient enough to achieve terminal velocity how high should the block of soft jelly be to dissipate the impact energy safely for an average human?

Answer 1

If you are going to survive hitting something at high speed it is not enough for that thing to be soft, it must also be light (low density).

To see why this is imagine falling into water. Suppose you hit the water at terminal velocity, which is around $50$ m/s. To enter the water your body has to push aside the water that's in your way. Specifically it has to push aside a mass of water roughly equal to your own mass (since the density of humans is roughly equal to the density of water). And travelling at $50$ m/s you have to push aside this mass of water in around $3$ milliseconds. That means the acceleration of the water is going to be very high so from Newton's second law the force required to accelerate that $70$ kg or so of water is going to be very high. The problem is that Newton's third law tells us that when you exert the force on the water the water exerts an equal force on you, and that force is likely to prove fatal. I don't know what the survival rates for freefalling into water are, but I strongly recommend you don't try it.

This is the problem with your jelly, since the density of jelly is very close to the density of water. The force exerted on you when you hit the jelly is going to be dominated by the force required to accelerate the jelly out of your way and the elasticity of the jelly won't have much effect. There is going to be little difference between hitting the jelly and hitting water, and both are likely to be fatal.

The cushions used to stop falling stunt men are filled with air because air is light. The pressure of the air can slow you gradually while the low density of the air means it requires little force to push it out of the way. Air also compresses, which a trick liquids and solids cannot do. Alternatively as discussed in Can a Skydiver Land On a Large Slide and Survive? you could fall onto some contoured surface that decelerated you slowly.

As Bob discusses in his answer, if you know the maximum deceleration you can survive then it's easy to find out how thick the cushion has to be since we can use the SUVAT equation:

$$ v^2 = u^2 + 2as $$

In this case the initial velocity $u$ is the terminal velocity and the final velocity is $v$ is zero so the distance required is just:

$$ s = \frac{u^2}{2a} $$

The redoubtable John Stapp showed that it is possible to survive $45g$ under ideal conditions so suppose we take $50g$ ($500$ m/s$^2$) as a maximum survivable deceleration. Then with a terminal velocity of $50$ m/s that gives us a minimum stopping distance of $2.5$ m. But, that would have to be $2.5$ m of something like an airbag, not jelly.

Answer 2

Regardless of what it is that brings the person to a stop, in order for the person to survive, the average impact force that the person experiences needs to be less than the person’s threshold of injury. Assuming the person’s kinetic energy upon impact with the object is much greater than the person’s gravitational potential energy with respect to the ground at impact, we can apply the work-energy principle:

$$\Delta KE=\frac{mv^2}{2}=Fd$$

Where $m$ is the persons mass, $v$ is the persons velocity upon impact, $F$ is the average impact force the person experiences and $d$ is the stopping distance, i.e., the distance the person falls after impact. Clearly, the greater the stopping distance the less the average impact force;.

Hope this helps.

Answer 3

Here's a case where someone (barely) survived a 35,000 foot fall into deep snow, while trapped inside the tail section of a disintegrated airplane. Note, though, that the terminal velocity of a falling human body is about 120 mph. The tail section of an airplane is likely to have a substantially slower terminal velocity because its density is much lower than that of a human body.