Velocity vs. Gravity

Neglecting aerodynamics, since the gravity vector is constant both bullets should fall the same distance in the same time.

Correct, and the grain size of the projectiles do not need to be of the same mass, either.

due to the curvature of the earth, the bullet has to fall further than the bullet that is droped vertically, this comes into effect more noticably at altitude. ie a satelite is asicly "falling around the earth, but due to its height and velocity cannot actually hit the earth.

I would love to see that test espically how you would find the very spot where the bullet fired from the gun hit the ground. When figuring changes in wind resistance or drift along with gravity and friction to calculate for over a miles. Alll of these and not to even mention the effects of worn grooves from the barrel on the projectile it's self, or a warped barrel from excessive heat caused by rapid firing.

Not to mention the fact that the impact zone is very likely at a different altitude from the gravitational center. If you include enough variables then you can never know the "exact" landing point of the fired projectile. However, by using an ENIAC, a little calculus, mix in a little Monte Carlo theory and you can establish an area in the shape of an ellipse and predict with a high degree of certainty that an infinite number of rounds fired from the same weapon will definitely fall within the confines of the predicted ellipse. Nevertheless the vertical distance traveled by both projectiles will essentially be the same and covered in the same period of time.

ive heard of this question before, and the answers were all over, there are to many different things to take into the picture, its hard to think the bullet thats dropped would take as long to hit as the bullet going at a very high volisity, since some of the bullets out there now can go for hundreds of yrds and only drop very little, but at the same time its because the speed is so fast that they dont have time to drop as far,, so its one of those things