As Itmauve alludes to, by not binding the pillows together at all, you allow the pillows beneath you to be shoved aside as you fall into them, which would mitigate this issue at least partially.

@anaximander The issue is that to shove pillows aside you must transfer them your energy. To send a mass equivalent to yours fast enough than they free the way for yourself, means transferring almost all your kinetic energy to them. The problem is not that pillows are bound, but that their mass will crush the jumper as he accelerates them to the sides.

I don't understand the numbers and assumptions in this answer. An average pillow weighs 3-5 pounds, nowhere near 10% of body weight. When you compress a stack of pillows, you don't accelerate the whole stack uniformly (the bottom pillow barely moves). The point about losing half the velocity within 1m seems to be predicated on the idea of the person falling onto a solid but moveable block that weighs the same as them. I see no reason why you couldn't compress a stack of pillows by more than a meter.

@NuclearWang the answer refers to a human-shape landing - i.e. one layer of pillows on which you can land on horizontally. If you land on one pillow lying down most of you is going to miss the pillow. 3-4 pillows, approaching a reasonable value for 10% of body weight, seem like they would cover the required area.

@Gregor--reinstateMonica-- Why are we limiting the stack size to the weight of the jumper? This isn't the classic inelastic collision case where a moving object colliding with a stationary one of equal mass moves away together at half the speed. The pillows are compressing, the bottom half of the stack accelerates much less than the top. Adding more pillows at the bottom of the stack doesn't change much about what happens when the person hits the first pillow on the top of the stack.

@NuclearWang excellent point... not sure why I just accepted that premise.

I've slept on some pretty darn fluffy feather pillows. I didn't find them pleasant, but they were described as "luxury" and I'm sure were expensive. 10m is a lot, but on consideration I won't rule it out.

@spectras That seems to approximate a situation where you're falling onto stone blocks, not pillows. Pillows bend and compress - none of the pillows except for the ones directly underneath you will accelerate to the same speed as you (as a whole). I don't understand the point about being "crushed" - the pillows get pushed out of the way with the same force as the initial impact, which is either fatal or not in the first place. How can someone falling vertically be crushed between two objects that are moving horizontally away from them?

@NuclearWang I'm not saying the jumper is crushed between two objects.

Yes, I was curious about @spectras comment about being crushed.

@NuclearWang I'm not limiting the stack weight, I'm trying to find the optimum case for the jumper and showing it's still very dangerous. Taking a slice of the stack equal to his weight makes the math simple and I much prefer to keep the math to a minimum to make it easier to follow.

@NuclearWang. Before even considering the compression of pillows below the next layers, just look at the top layer. Say they are 20cm thick. That means by the time the jumper has traveled those 20cm, he must have pushed all pillows of that layer away. That is about 7ms. Unless the pillows are unrealistically light, the required force is large.

Perhaps it's easier to picture it like this: imagine a bunch of pillows, just enough to make the shape of a human body, floating around in space. Now, throw someone into them at 100km/h. They will be hurt pretty bad, assuming a regular pillow (what matters is a combination of its mass and its ability to bend and compress - pillows are just too dense).

The deceleration can be decreased by jumping legs first and pushing the pillows aside. That way they'll need to move a lot slower to get out of the way, so they'll absorb less energy. They are still denser than the preferred material to fall into, the cardboard boxes though.

@JanHudec 5g on your back is very different than 5g standing. I don't think he'll remain in that orientation when he hits.

@LorenPechtel, I think he will, just like those who jump into water do. Straw would probably be better than pillows though since the cloth wrapping the feathers of the pillows will make them spread non-uniformly.

@JanHudec Going into water from this height is usually lethal.

@LorenPechtel I see what you're saying. After thinking about it some more, I think that simply the density of the pillows plays a big role, as you're right, more massive pillows will require more energy to move/compress, and if that energy change happens in too small a distance, it will be lethal. Using super-fluffy (low density) pillows is a must, and it might be best to have a loose stack with air gaps - that way, compression can happen over a longer distance, and you can be slowed by corners and edges that will subtract less than one full pillow's worth of momentum from your fall at a time.

@LorenPechtel, yes, but water is also much denser than feather pillows or straw. The point is that you can jump to water legs first from much higher than flat, and that will apply to other materials that can move out of the way to the sides as well (for a net it won't make much difference).

@NuclearWang I'm not sure I do understand what that's getting at. The taller your stack of pillows, the more give the pillows on the top will have (see springs in series for a good example of this). Pillow compression isn't really based on the mass, but on it's resistance to deformation, and the more you stack, the less the pile resists this deformation. So yes, you want the right level of "give" to the pillows; but that can be achieved by using lighter fluffier pillows, but it can also be achieved by just stacking them higher (with diminishing returns as the self-compression kicks in more)

@JMac Take a stack of pillows of some height. When you fall on it, some of your momentum is transferred to the pillows, accelerating them downward. If that stack of pillows is very light, you don't have to transfer much momentum to get them to compress. If that stack is very heavy, it'll require more momentum to move them, lowering your own velocity much faster, resulting in larger (potentially harmful) g-forces. Imagine you land on a water bed at the top of the pillow stack - it's squishy, but the sheer mass of the water means the bed won't move much (rather, it's you who will stop moving).

@JMac It's kind of like taking two springs with identical spring constants, but one spring is much more massive than the other. Both have equal spring resistance, but if you drop the same weight on both, the massive spring will compress less, since the object's gravitational potential energy now has to be split between the spring potential energy and the spring's kinetic energy, whereas the low-mass spring converts nearly everything into spring potential by compressing more, since the low-mass spring's KE is negligible. The pillow's springiness is not the only factor, its mass plays a role.

@NuclearWang Thanks, I see what you're saying now. I still don't really agree with this answers assumptions about pillow fluffiness and stuff though. It uses some "best case scenario" logic; but then seems to mix it with more of a "worse case scenario" of heavy pillows; so the picture it paints doesn't really rule out survival for me.

@JMac Agree, people have survived much worse, so I'm definitely not ruling out survival either. At any rate, it's been interesting thinking through the factors that would affect the odds of survival/injury, even though I'm not much closer to deciding if severe injury or complete success is the more plausible outcome!