Well, the math of how fast it’s going when it comes back down has nothing to do with how far up it goes. Without air, it reaches its starting height at the same speed it left (just with the opposite vertical vector). The problem is figuring out the terminal velocity which depends on the surface-to-mass ratio, the shape, and in the specific cases, the winds which could prevent the bullet from assuming the most efficient orientation and could provide up &/or down acceleration. It sounds like (from the army experiments) that, (maybe) depending on the bullet, it would probably penetrate your skin, maybe break a bone, and if it hit dead center of your head, kill you. Just a not-so-WAG.
You guys trying to use gravity equations to figure this stuff out are missing an important point - at ground level, atmospheric effects grossly distort the ‘true’ ballistic path of the bullet, and wind resistance is by far the most important part of the equation.
For the purposes of figuring out how fast a bullet drops, the only thing that matters is its terminal velocity, because even low-power bullets will go high enough to reach terminal velocity on their way back down. And the terminal velocity of the bullet is dependent on its mass, and its cross-sectional area and shape. And of course, whether or not it’s tumbling.
My WAG is that a typical bullet (say, a .45 caliber FMJ round-nosed bullet) could possibly crack your skull if it hits it, but probably wouldn’t kill you. On the other hand, a depleted uranium flechette with vanes would probably punch through you like butter. I wouldn’t be surprised if it would punch through a car.
Coriolis force is also irrelevant for this discussion, because wind will have a much, much bigger effect on the bullet. And even if it’s calm on the ground, at a mile or two up the wind’s probably cooking along at least 10 or 20 kts, meaning the wind will throw the bullet hundreds of feet off course.
As for people being hit with falling bullets being ‘common’, I suspect that it’s fairly common in some Arab countries where guns are fired in the air in celebrations. I’ve seen videos of parades and demonstrations where dozens of people were firing full-auto into the air until they emptied their clips. That’s maybe 20-40 bullets per person, fired into the air in a crowded street. Hundreds of bullets falling back to the ground. That people would be injured or killed regularly in such situations wouldn’t surprise me at all.
I always assumed that a bullet shot more or less straight up would tumble on the way down. However, today I considered that bullets spin due to the riflering in the barrel and the spinning of the bullet would possibly continue after turning around at the highest point. If that is the case, I would imagine that the bullet would be in a very streamlined position on the way down.
I haven’t checked any links yet, but does this sound plausible?
In the link above, describing the U.S. army experiment, it says that a bullet that hit the wooden platform hit butt-first.
Given the shape of the typical bullet, the center of mass is probably below the midline of the bullet, which means it would tend to fall butt-first when it comes back down. Just my WAG.
By the way;
Shouldn’t it be called “terminal acceleration”? The object doesn’t stop moving, it just stops going faster than it was before.
Seems to me that tv would be when it struck you in the head. Impossible though that may be.
Peace,
mangeorge