Can a bullet fired up into the air injure you when coming down?
Yes it can.
That said a bullet fired straight up will fall back down at its terminal velocity of around 300 fps so it doesn't have anything close to its muzzle velocity. Another factor is that when the bullet reaches the point where it begins to fall it looses stability and will begin to tumble making it more likely to roll off of anyone it might hit. Finally if the bullet hits on its side, the bigger surface area means less PSI on the contact area.
But if the bullet is fired at an angle where it flies in an arch it will be traveling much faster and is far more likely to injure or kill someone. Likewise it will maintain stability and strike point first.
The last thing to consider is what caliber the bullet is, or rather how much they weigh. A .45 bullet would be far more likely to hurt someone than a .30 caliber and a .22 bullet might not be any worse than a small hailstone.
A number of injuries and deaths are recorded for falling bullets every year around the world but these statistics don't differentiate between bullets fired straight up vs those fired at an angle so they aren't very accurate in answering your question.
Yes it can. If you shoot a gun straight up in the air, when the bullet loses it's momentum because it is fighting gravity, it stops going up. At that point, gravity pulls it down, and it can hit someone, and of course, injure them.
Unquestionably, a bullet fired in the air at any angle poses a threat of injury on descent. I have seen bullets fired into the air at an angle from a great distance puncture a corrugated metal roof. One rifle bullet fired directly overhead struck a young man's helmet some distance away, and it dented his helmet.
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