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This begs the question for me - at terminal falling speed, what's the fastest you can decelerate to 0 and not sustain injury? And given that, how much more distance would you need to move?
Maybe a superhero can catch you, decelerate you to 0 over 3 inches and that's good enough?
Human terminal velocity is roughly 56 m/s. Let's say our superhero wants to decelerate the person at 10G, which should be survivable for a short period. That would be 0.6 seconds of deceleration over 48 m. That's a short time but quite a long distance, let's slow down faster:
20G -> 0.28 seconds, 24 m.
30G -> 0.19 seconds, 16 m.
50G -> 0.11 seconds, 9.6 m.
100G -> 0.057 seconds, 4.79 m.
200G -> 0.029 seconds, 2.45 m.
5000G -> 0.0011 seconds, 3.6 inches.
A 40 mph car crash in a modern car into a solid wall gives around 15G.
F1 driver David Purley survived a 180G crash in 1977.
In short, I don't recommend catching someone with 3 inches to spare.
Something is wrong with your distance formula by a factor of 4 (you should have D=1/2 * V_0^2 / a) . Not that it changes anything in your conclusions.
The same forces but concentrated onto our heroes arms. Very efficient way to slice
The slicing forces would actually be helpful, because the resistance of the arms would spread the impulse out over a longer time period. So maybe you get decapitated, but your head doesn’t just instantly splat. So you get… a few seconds? more of life.
our hero's* arms
I came here looking for a The Boys comment about the plane, but noone talked about it 😓