# Bullet Fired Straight Up

If a rifle bullet were fired straight up, approx. how high would it go? (No doubt it depends on the rifle and the bullet and probably lots of other things. I’m looking for a ballpark estimate, not a precise answer.)

## If you neglect air resistance, the maximum height of a bullet fired straight up is V^2/(2g), where V is the initial (muzzle) velocity of the bullet, and g is acceleration of gravity (9.8 m/s^2). The initial velocity of a typical rifle bullet is about 300 m/s, so the maximum height in meters is (300300)/(2*9.8) or 4592 meters, which is 15000 feet or about 2.8 miles.

“For what a man had rather were true, he more readily believes” - Francis Bacon

There can’t really be a ballpark estimate, because it depends on the gun. Anywhere from a mile for a .22 LR To who knows what for some real big calibres. Maybe 10 miles?

Muzzle velocity is a limiting factor. According to my calculations (as described by Mark Mal) a muzzle velocity of 1000 ft/sec would top out at about 3 miles and 2000 ft/sec would go about 11 miles, neglecting air resistance.

Air resistance is in no way insignificant, though, and would easily cut these numbers by half, or even more.

## Incidentally you can see that doubling the muzzle velocity more than doubles the height attained. If my figures were more accurate the height would go up as the square of the velocity.

“The inability of science to grasp Quality, as an object of enquiry, makes it impossible for science to provide a scale of values.”
Robert Pirsig

And 2000 ft/sec muzzle velocity is closer to “average” than 1000 ft/sec. The .22-250 maxes out at about 3750 ft/sec. Pretty damn fast.

“The problem with the world is that everyone is a few drinks behind.” - Humphrey Bogart

In the same way, what speed must an object travel in order to escape the pull of the earth i.e. the escape velocity? I rememeber being able to calculate it a long long time ago…brain no use anymore. It’s independant of mass right?

Yes, my brain function is independent of mass. Or at least rest mass.

Escape velocity from the surface of the earth is 11.2 km/sec or about 7 mi/sec or 25000 mph.

TheDude

I’d get you a ballpark answer but the ballparks around here are all within the city limits and the authorities frown on firing weapons within city limits.

Ray (Guess I better try to achieve that 25,000 mph escape velocity about now.)

The faster the bullet goes, the more important air resistance is going to be, but since it will go higher, it will have less drag on it at the top where the air is thinner. It would be a pretty complex function to model it accurately.

You could just assume a constant air drag. That would be good for a first approximation. I’d do it myself, but I have real work to do.

“I had a feeling that in Hell there would be mushrooms.” -The Secret of Monkey Island

“Pretty dern high.”

That would clasify as ballpark estimate, wouldn’t it?

Oh, come on, Chief! You’ve got guns – lotsa guns of different types. You’ve got miles and miles of open sea. You’ve got tracer bullets. You’ve got the most sophisticated tracking equipment in the world. You’ve got time.

Help out the Teeming Millions here!

Livin’ on Tums, Vitamin E and Rogaine

Okay so that bullet goes up. It has to come down too. When it does, how deep does it go into thee ocean?

That depends on how high it went in the first place.

Actually, I suspect that it depends more on how deep the water is.

Livin’ on Tums, Vitamin E and Rogaine

Handy: Unless you have some kind of bizarre floating ammunition, the bullet will stop at the bottom of the ocean.

“I had a feeling that in Hell there would be mushrooms.” -The Secret of Monkey Island

I think the Teeming Millions test this all the time… during Seafair last summer at Sayre’s Pits on Lk. Washington the medics treated a guy who had been hit in the back of the neck by a .22 bullet- the entry angle was straight down.

It continues to crack me up that he was wearing a “Lucky Strike” t-shirt.

“You can’t tell me what sucks!” - Beavis, a true Objectivist

OK, extra credit question time: If a bullet is fired straight up, and there’s absolutely no wind, will it come straight down and hit the shooter, or will the earth’s rotation cause it to miss the shooter? Or does the fact that the barrel of the gun has the same rotational motion as the earth negate that?

If the shooter was standing at the geographic north or south pole, the Earth’s rotation wouldn’t come into play thereby stiking the shooter square in the melon.