Wrong answer, Cecil. All guns fire bullets on an arced trajectory. The bullet floats up a bit before it begins to fall. As such, the dropped bullet hots first, as it has less of a vertical fall to make.
…so doesn’t that mean that the bullet wouldn’t “float up” at all?
Assuming a vaccuum, and assuming that the barrel of the gun is perpendicular to g (the gravitational vector), then Cecil is, as always dead on.
A bullet will only rise if there is air for it to push against.
-andros-
In Cecil’s column (Beat ya, Arnold!), the question states explicitly, “aimed so it’s perfectly level”. In other words, it’s not an arced trajectory: Maybe that’s usually the case with guns, but it isn’t here.
Of course, Arnold never provides the link when someone else already has. Best to leave these things to the professionals, Chronos. 
Not too sure what causes the arc… if it were simply air pressure, I would think it would/could affect the round from any direction – i.e. it could be pushed downwards, sideways, etc. And you see this even in guns that are held “perfectly level.” So what causes the bullet to arc?
Contrary to popular belief, when the Teeming Millions post a link before I do, I don’t wail and gnash my teeth, but I thank them for a job well one, and saving me some work!
Thank you Erroneous and Chronos.
The column can also be found on page 201 of Cecil Adams’ book “Triumph of the Straight Dope”.
I don’t know why Cecil is “assuming a vacuum.” But assuming a vacuum the gun would not fire, because combustion would not occur. The bullet would go nowhere.
touche
He’s assuming a vacuum because air complicates the issue. Plain old friction can be resolved into independent components, and thus cancelled out (the verticle component of friction is the same for both), but turbulent effects could in principle change the answer in either direction. Also, of course, if you’ve got this thick soup of an atmosphere, you can’t make the generalization to orbits. Given that we’re assuming a vacuum, I think it’s also safe to assume a gun capable of firing in a vacuum. This could be done: Replace the powder with solid rocket fuel, say.
Don’t need to change the powder at all, it already contains an oxidizer. Think about it, how would sufficient air get into the cartridge in the time it takes to fire a bullet.
What you have to change is the lubricant, since petroleum-based lube doesn’t work in a vacuum (I understand it hardens). I think they use graphite-based lube on spaceprobes, so that would probably work for guns too. But I’m not a rocket scientist, so I could be wrong on this.
I maybe wrong (I often am)but is everyone overlooking rifling? Like when a quarterback throws a long pass the spin on the ball helps it resist gravity longer. Bullets travel the same way. So assuming a vacuum, and a gun made within the last hundred years, the fired bullet would take longer to reach the ground.
cringes for impact
Sorry, rifling will only help in an atmosphere. Take that spinning football. The spin on the football stabilizes it so that it doesn’t tumble. A tumbling football will have higher air resistance, and thus fall to earth quicker. The same thing happens to bullets, which is why they put in rifling in guns.
But remember this is a vacuum we’re talking about. There is no atmosphere, so it doesn’t matter if it’s tumbling or not. I expect that a gun made specifically for use in a vacuum would not have rifling as that reduces the muzzle velocity.
I think I should clarify this. By falling to earth quicker, I mean that the range will be shortened, not that it will be in less time. But spinning or tumbling could have other aerodynamic effects that could change the time that it takes to hit the ground. Consider the effects of spinning on a curve ball, for example.
Here’s why:
(Again, assuming a vaccuum, that the earth is a perfect sphere, and we’re firing perfectly parallel to the tangent.)
The earth is curved, so the earth is measurably, albeit imperceptibly, dropping away from the tangent.
The “fired” bullet will therefore land the smallest fraction of a second after the “dropped” bullet.
Oh well.
Mjollnir,
I’m not sure who’s still wrong. Cecil covered that effect in his column.
Alas, Cecil is AGAIN wrong.
“If the fired bullet travels only a short distance, then yes, both bullets hit the ground at the same time.”
Wrong, wrong, wrong.
As Mjollnir has already pointed out:
"(Again, assuming a vaccuum, that the earth is a perfect sphere, and we’re firing perfectly parallel to the tangent.)
The earth is curved, so the earth is measurably, albeit imperceptibly, dropping away from the tangent.
The “fired” bullet will therefore land the smallest fraction of a second after the “dropped” bullet."
Even if it’s fired a tiny, tiny distance, the bullet would still hit the ground after the dropped bullet.
Also, as Sneevil has already mentioned.
“I don’t know why Cecil is “assuming a vacuum.” Assuming a vacuum the gun would not fire, because combustion would not occur. The bullet would go nowhere.”
Cecil is wrong, yet again. I wonder if he will actually admit it this time? HAHAHAHAHAHAHA!!! What was I thinking???
First off, the only reason a bullet or whatever would travel in an arc is if gravity or a strong wind were acting on it. Hang from the ceiling of a room with no air gaps and fire a bullet straight down and tell me if you see it arc. Go to outer space and fire a bullet (yes it will fire because as dtilque already pointed out it has its own oxidizer) and see if you can detect any arc (within the limits of Newtonian mechanics). Now, if the Earth had a reeeeaaallly featureless surface(completely uniform, but really the Earth could be egg shaped for all it matters, as long as there are no VALLEYS or FLAT surfaces, you get the drift?), then you fired the gun at a completely parallel angle to earth, and no wind was kicking up, and the the bullet was not tumbling (though I think that would probably affect distance more than falling time)then yeah, the dropped bullet would hit the ground first because of the curvature of the earth. But if you just made a completely flat surface in a total vacuum but still had a constant gravity, then both bullets would hit the surface at the same time. Make sense??
Correction to my last post: After further brainpower being devoted to the issue, I realize that the Earth would in fact have to be perfectly spherical to make the experiment work as I stated. Props to Mjollnir on that one.