Anybody still read newspaper comics these days? I do, but sadly for the newspaper business I read them online. Worse, usually in the context of people making fun of them. On the other hand, there are a few gems out there. Is Spider-Man one of those gems? Uh…
Well, Shakespeare it ain’t. But is Spider-Man justified in his optimism about being able to catch Mary Jane? If Doc Ock just drops her instead of throwing her (as he seems to suggest), she’ll start with zero velocity and immediately begin to accelerate at 9.8 meters per second squared vertically downward. As soon as Spider-Man jumps to catch her, he’ll do the same thing. To his advantage he’s got webbing he can shoot to catch her right away, he doesn’t have to do the classic Superman catch. Regardless of how he stops her, he has to do so smoothly and gently. It’s a cliche but true nonetheless that it’s not the fall that kills you, it’s the stop. With plenty of time to catch her it’s not a problem and I think she’d be safe here.
But what’s more interesting is the worst-case scenario where our superhero is standing at ground level and has to catch the falling victim. It’s a frequent conceit, but how realistic is it. Turns out, not very.
The velocity of an object falling from a distance h is:
This has to be reduced to zero before the victim hits the ground. The acceleration necessary to do this over the short distance between the point of catch and the ground (call it x) is:
Both of these equations come straight from the standard laws of 1-d accelerated motion. Substituting the equation for v into the equation for a, we get:
It’s a simple equation, but a telling one. A human being wearing a seat belt in a car crash can generally sustain around 15 g’s worth of acceleration without serious injury. Beyond that we rapidly climb the thresholds of serious injury and death. But the equation tells us that the required g force to stop the victim before hitting the ground is just the ratio of the initial fall height to the stopping distance. If Spider-Man brings her to a stop in 1 meter, she had better have fallen from 15 meters or less if she wants to escape injury. It doesn’t matter how super-powered he is, that’s just physics. If she falls from hundreds of feet, she’s dead unless the catching process begins well above the ground.
Interestingly, the comic book Spider-Man is one of the very few characters who have actually dealt with this realistically – at least once. The comic book Gwen Stacy character dies when Spider-Man catches her too abruptly, killing her. Nobody said physics was always fun.
[At least a few of y’all did a few Amazon.com purchases from this site’s link yesterday. Thanks, and thank you if any of the rest of you do it in the future! It’s greatly appreciated and will go a long way. -Matt]