for physics/math people: how high would a bullet go if shot in the air? (1 Viewer)

[DaveF]

The bullet will reach one to three miles before falling back to earth.

Basic equation for motion:
D(t) = d + v*t + 1/2*a*t^2

where
t = time (sec)

do = initial height = 0 m

v = velocity of bullet out of gun = 300 m/s (~984 ft/s, based on Philip's info)

a = gravity = -10 (-9.81 m/s^2 really) (gravity)

d = distance as a function of time

Wind resistance ignored.
Motion assumed to be perfectly vertical.

Employ some calculus and solve for maximum distance:
D'(t) = d/dt D(t) = v + a*t
D'(t) = 0 = v + a*t (at max)
v = -a*t (at max)
tmax = -v/a = - 300 / (-10) = 30 sec

Max distance:
D(tmax) = 0 + 300*30 - 1/2*10*30^2 = 4500 m = 4.5 km = ~ 2 miles

Get a freshman or sophomore engineering student in here to check my math. I've not done this for homework in over a decade

 

[Jeff Gatie]

No, I liked them. I just knew they were not applicable to the real world, hence I became an engineer. My HS physics teacher used to have a thing called the "bump factor", where each kinematics experiment was given a small "bump" to factor in all the stuff we ignored. Got the ball in the cup (or whatever the "successful" experiment was) every time after the "bump factor" was applied.

 

[DaveF]

Phill - you snuck in your answer while I was typing mine!

 

[D. Scott MacDonald]

As others have correctly stated, the muzzle velocity only matters if the gun was fired in a complete vacuum and the bullet was allowed to fall without any outside forces besides gravity, in which case the bullet would land with the same velocity at which it was fired.

In practice, it's all about terminal velocity. For example, in theory a human falling should continue to accelerate as they fell, but in practice they max out at around 120 MPH (my number here may be off by 40 MPH or so, but that's about what I remember).

Likewise, the Mythbusters tested to see if a penny dropped from the empire state building would actually kill somebody, and they measured that the terminal velocity of a penny is between 30 and 60 MPH (it has much less mass and it's shape causes it to tumble and interact with the air much more than a falling human would). They determined that a 60 MPH penny would not cause serious harm to a person.

When a bullet leaves the gun, the rifling makes it spin and keeps it streamlined against the air. I suspect that when it reaches 0, and then starts to fall, it would also start to tumble and interact with the air a great deal (although much less so than the penny). I have no idea whether such a bullet would be lethal or not, but I suspect that it would be heavily dependant on it's mass.

 

[Philip_G]

physics is fun, math isn't

 

[NickSo]

okay, reading all the formulas i regret posting this here... :p)

now i remember why i didnt take physics 11/12 in high school

 

[Glenn Overholt]

All of that math is giving me a headache!

Your other question is yes, people have been killed from falling bullets.

I can't remember where/when exactly, but it has been on the news a few times. Some cultures celebrate by firing guns into the air - a truely insane idea.

I keep on thinking Afghanstan after they were freed, but weedings and New Year's Eve also comes to mind.

I've seen people do the arrow thing - there would have to be ZERO wind, and the arrow would be tumbling when it changed direction (from up to down), so having it land in the same spot is unlikely.

Glenn

 

[PhillJones]

The bullet from a gun doesn't stay pointing forward just becuase it was in that orientation in the barrel. It does so because it's the orientation of least resistance. It doesn't really matter, which orientation the bullet starts off in, it'll align itself very quickly.

I would imagine a coin is a bad shape for drag, the sharp leading edges would liekly set up vortices at the side and make for poor air flow.

 

[Greg*go]

off topic..

I liked that episode. If what you are saying is your main complaint, then why bother with the experiment? Even if they used the same automobile, you could argue that it would yield different results with a different car. Plus No two drives are the same either. You can argue that when the first drive ran out of gas, it messed up the engine for the second drive.[/rant]

Back on topic, this is what google has to say about the origianl question:
http://www.villman.com/forums/topic.asp?TOPIC_ID=1087

It talks about a couple people that have tried it too and I found the results interesting.

 

[Andrew_Sch]

Somebody got killed by a bullet fired into the air in an episode of Homicide: Life on the Street, which is a pretty realistic show.

 

[Philip_G]

How can you have a controlled experiement with two vehicles that could produce wildly different gas mileage figures? The point of the experiement was to determine which was more fuel efficient, they dumped in 5 gallons of gasoline, and drove at ~35 mph around a track, the smart thing to do would be to run the tests in the same vehicle back to back.
the experiement is so small that even a small error could create very different results.

 

[EugeneR]

Yeah, they're called Angelenos. A number of people in L.A. have been killed over the years from bullets dropping from the sky. Around New Years, we always have Sheriff's Dept warnings on posters and TV to not celebrate by firing guns into the air. We are therefore confined to shooting fellow motorists on area freeways to compensate for the Man infringing on our right to self-expression.

 

[Joe Szott]

You could make that arguement, but since that's not the way engines work it wouldn't make any sense! Run of oil yes. But out of gas? All you do is add more gas and the car is as good as it was 10 seconds before it ran out of petrol.


I agree with the engineers here, discounting friction and terminal velocity is a mistake, that's the whole equation for figuring out what's going on here. Essentially, heavier bullets with the same diameter (area resistance) will reach a greater Vt and become more lethal on the return trip. I would guess that almsot any bullet above a .22 would reach speeds to easily kill someone unlucky enough to be hit by it. Also, with the bullet falling from above, an upright person would be much more likely to get hit in the head and therefore be killed.

 

[Benny G]

You can blast a shotgun round into the air and the pellets fall harmlessly back to the earth. Just a couple weeks ago, my dad demonstrated that in back of my house. Everytime he shot into the air, you could hear the pellets gently hitting the roof of the house.

 

[BrianW]

When I fire my gun into the air, I do so discriminately.

 

[Yee-Ming]

Makes sense. Although I'd think that if the gun is shot at an angle, the bullet sort-of goes on a ballistic curve but stays pointed forward, regardless of whether the above applies or not.

Don't snipers actually have to factor this in as well? I.e. over the extreme distances they shoot, gravity will start "pulling the bullet down", so they actually shoot "higher" than at closer range?

Forgive the purely layman's thinking above, I barely passed A-level physics, and 18 years later can hardly remember any of it at all... :b

 

[NickSo]

heehe, i think i saw that episode before

 

[Jeff Gatie]

Gravity actually starts pulling the bullet down as soon as it leaves the barrel, although some bullet, gun and load combinations will cause it to rise first due to barrel specs and bullet type. I know the .270 round has an tendency to shoot a little high at 100-150 yds, then flatten out before it starts to drop. The reason you only have to compensate for the drop at longer distances is because the velocity of the bullet is so high the time for gravity to act upon it is very short at shorter distances. That does not mean gravity is not there at first. As someone once said to me "Gravity works, 100% of the time".

 

[Philip_G]

depends on the round, there are ballistics charts for most rounds widely available online with a little searchig. You can roughly assume to be "on" at 200 yards you'll be 2 or so inches high at 100 yards though.

 

[Linda Thompson]

An old discussion of this topic (and a couple of tangents) from Cecil Adams' "The Straight Dope":

http://www.straightdope.com/classics/a950414b.html (not nearly as technical or scientific as the excellent Villman item which Greg referenced above)

http://www.straightdope.com/classics/a5_201a.html

http://www.straightdope.com/classics/a881216b.html

http://www.straightdope.com/classics/a1_225.html


A spirited forum discussion:

http://www.thefiringline.com/forums/...p/t-72436.html