I don’t know if this video tells a real story or not, but it inspired me to ask a question:

Let’s suppose a human being is either falling out of the sky from an arbitrary height (maybe even space) or is for some reason moving really fast (maybe he was shot from a human cannon or something) and he doesn’t get seriously wounded from the motion itself. Could a cushion be designed such that this person would survive no matter how quickly he or she was moving?

Would a 100 meter square cube (with open top) of cotton accommodate any fall? Nevermind getting the person out of the huge cotton mass of course, you know what I’m asking.

For falls from heights, movie stuntmen generally use big airbags that deflate when they land on them. This is probably the way to go to do what you have in mind. It’s just a matter of being able to make a big enough airbag.

And since there is a finite limit to how fast you can fall, no matter what the height is, it should be a simple matter for them to work it out. Of course you would need to make sure that you hit the cushion.

so how does the formula for the height of the airbag based on the height of the fall look like? E.g. if we want to fall from 5 miles, how high would the airbag have to be?

Your velocity stops increasing after you’ve fallen 1000 ft or so. If you are falling belly-to-earth it’s around 120 mph; headfirst, it’s something like 200 mph.

Here’s a nice cite supporting that assertion: Speed of a skydiver
In it, one finds the report of a skydiver who hit 614 MPH while falling at 100,000 feet. He of course slowed down as the air thickened.

I think the key point of the question is the “really fast” part. Don’t limit to terminal velocity due to gravity, imagine maybe a malfunctioning jet pack (Toyota was in charge of its accelerator button :)). The question is can a the right cushion decelerate a body within acceptable survivability limits for any arbitrary approach velocity?

And of course one can design a “cushion” to slow down any arbitrary particular object at any arbitrary particular velocity at any arbitrary particular rate so long as one know all the particulars in advance.

If you have the technology to accelerate to a significant percentage of c, surely you have the technology to make an airbag that is a significant percentage of a light-year long. Of course to slow down at a safe rate from c, it would be less an air bag, and more a galactic sized fart.

When you describe the person as moving arbitrarily fast, do you mean with respect to the cushion or with respect to another arbitrary point of reference? If you can have the cushion moving in the same direction as the person but at a slower velocity, then I would think you could cushion any impact. If the person is moving fast enough relative to the cushion, however, wouldn’t you eventually reach the point where atoms colliding is too destructive for the person to survive? My knowledge of physics is elementary at best, though, so I’m sure someone will correct me.

Let’s assume that you can tolerate a sustained acceleration of 10 g’s applied to one side of your body, and that you are clever enough to design a cushion that uniformly decelerates you at that rate, independent of how fast you are going. The only limitation is the thickness of the cushion. The required thickness is given by:

t = v^2/2a where a = 10 g, so t = v^2/20g

Putting in numbers, if you are going 100 miles per hour, you need a thickness of 10 meters or ~30 feet. If you are going at 1000 miles per hour (Mach 1.3), you would need 3000 feet.

If you are going at orbital velocity (~17,000 miles per hour), it would take a cushion about 200 miles in thickness. That’s in the ballpark of the length of the burn of the space shuttle putting people into orbit. Thick of the space shuttle as solving the inverse cushion problem.