# bullets shot upward then falling

I heard a newscaster warn the public against shooting guns up in the air to celebrate New Years (what the hell has the world come to?) and say that a bullet shot straight up in the air will return to earth at the same speed. Something tells me this is not right, and something tells me this is right. (That’s what I REALLY know about physics - some stuff is intuitive, but some is counterintuitive, and intuition wont help tell the difference). I know that one answer will entail considering air resistance (the REAL answer), and one will be a theoretical air-free type of answer (the REAL answer). Any help?

I think the gist is that terminal velocity for a bullet is not very high, and wouldn’t kill you, but it’d hurt like a bitch.

Easy one. The bullet returns to Earth at the same speed it left the gun, in the absence of air. Since we have air, this isn’t the case in the real world. Instead the bullet falls at its terminal velocity, the velocity at which the drag force on it due to air is exactly equal to its weight.

Terminal velocity depends upon many things, the density, shape and size of the bullet. A little .22 rifle bullet hitting you on the head might make you swear a bit but is unlikely to do any real damage. A .50 BMG bullet is another matter, not only because it’s heavier but also because its terminal velocity will be considerably greater.

Here is Cecil’s column:
Can a bullet fired into the air kill someone when it comes down?

And,matt, a bullet that falls from, say 1000 ft, will accelerate at 1 g on an airless Earth. It doesn’t matter how quickly it got to 1000 ft.

People get hurt from this type activity because the bullet is not typcially fired absolutely straight up. It hapens in the urban and suburban areas of California with too much frequency. I recall a case from Northern CA —I believe it was in either the Antioch or Sacramento areas— where a woman sitting outside preparing to watch the July 4th fireworks was hit in the leg by a rifle bullet. She didn’t hear the gunshot, so it took a moment or two to realize what had happened. By coincidence, a cop was on patrol some distance away and rounded a corner just in time to see some clown discharge his .30-.30 into the air in “celebration”. Since shooting a gun in city limits is against the law in most places —including there— the cop hauled his ass in. They correlated this report with the report from the ER of the lady being shot, and sure enough, ballistics tests showed a match. Clown was charged with inadvertently shooting the lady.

There is also a story (which I don’t know to be true or not) about a Pakistan International Air flight being shot down by guns fired by a wedding party. I am pretty sure it wasn’t a major size airliner in level flight at 30,000 feet or what have you; if it’s a true story, it’d probably have been a smaller plane (puddle jumper type?) flying lower, perhaps landing or taking off.

Perdabo: "And,matt, a bullet that falls from, say 1000 ft, will accelerate at 1 g on an airless Earth. It doesn’t matter how quickly it got to 1000 ft."

Sure! I didn’t mean that the bullet returns to Earth at the same speed it left the gun, ALL THE WAY DOWN. I meant that it will be travelling at the same speed it left the gun by the time it reaches the surface again.

A Los Angeles man was killed on New Year’s Day because of a bullet falling from the air. CNN has an article at http://www.cnn.com/2001/US/01/02/crime.guns.reut/index.html.

From today’s “Globe and Mail”, Canada’s national newspaper, a summary of American New Year’s Eve handgun fun:

1. In LA, police received 283 reports of gunfire between 8 PM and 4 AM New Year’s Eve. \$ people were wounded including a 10 year old boy hit on the head by a bullet that “travelled down his face and lodged in his cheek”. Benjamin Velasco. 31, died outside his mother’s home where he had dropped off his children to sleep for the night. “Wow, I think someone hit me” were his last words. There was no sound of gunfire.
2. In Cleveland, near midnite at a drunk driver check point, officer Dennis Lally was hit by a bullet on his leather jacket, just above his vest. It didn’t break the skin.
3. In New Orleans six people were arrested for firing guns in the air. In New Year’s Eve 1999 in New Orleans five people were hit by falling bullets for a total of 24 New Year woundings and one death since 1994.
4. In Laredo Texas a 14 year old girl collapsed and died just after midnite outside her home when hit by a bullet. Another woman in Laredo was struck on the thigh when a bullet penetrated the roof of her mobile home, but it did not penetrate the skin.

In Toronto, Canada, handguns are sometimes fired into the air at funerals. It’s called a “Jamaican salute”.

matt,
I think that since the initial acceleration up is much higher than 1 g, and after the bullet reaches the top of it’s path and has a velocity of zero, it begins accelerating down at a 1 g rate, the max speed is not equal to the muzzle velocity when it it reaches the muzzle. It would have to accelerate up at the same rate that it accelerates down for for the velocity to be the same, wouldn’t it?

Just to add to the anecdotal evidence …

When my beloved Alabama Crimson Tide played the Miami Hurricanes in the Sugar Bowl in 1993, the guy who wore the Miami mascot suit (Sebastian the Ibis) was hit by a bullet falling back to earth the day before the game. It cut his face below the eye, as I recall, and he required stitches, but he still performed at the game. He said something to the effect of “It would take more than a bullet in the head to make me miss this game.” I admired his spirit, even though he represented the opposing team.

Sadly for him, Alabama beat Miami 34 - 13 in that game.

I think, if I remember my physics class correctly, the velocity will be the same because the muzzle velocity upon firing has an effect on how high the bullet goes in the first place. Specifically, as the bullet is flying upward, it is accelerating at -1g (being pulled downward by gravity). It reaches a point where the acceleration is 0, and then begins accelerating again at 1g. Since the acceleration is the same (but opposite), over the same distance, the velocity will be the same when it reaches the point from which it was launched.

Keep in mind that this is what happens in the absence of air resistance!

troub’s got it, although I’ll be picky and point out that the velocity reaches zero at the top of the bullet’s trajectory, not the acceleration.

The situation is symmetrical. The bullet starts off at e.g. 3200 ft/s going straight up. It decelerates at 1g all the way up, ending at zero ft/s, 160,000 ft in the air, 100 seconds later. It then accelerates at 1g all the way down, ending up at 3200 ft/s by the time it reaches the ground.

This is very far removed from what actually happens because atmospheric drag totally dominates the behaviour of fast projectiles in the real world. it isn’t even a good approximation! Makes the maths simple though.

[hijack]

I’ll bet that Butch Davis was wishing this would have happened sometime last night (before the 4th qtr.) I know if Miami was not already up by 16, there would have been several bullets in the head after the game.

Last week the TV news was covered with stories about funerals in the middle east, and always showed the soldiers in the procession shooting blindly at 45 degree angles, just to make noise.

Another picky point worthy of note however if you ever work for NASA. The force on the bullet due to gravity remains constant. It is the weight of the bullet which is always positive in the downward direction. Since force is proportional to acceleration due to gravity, then it stands to reason the g remains positve. (They are both vectors). In other words the ascending bullet travels at g acceleration as well.