drop of a bullet vertically vs. horizontally
 

My physics teacher told us that if you drop a bullet and fire a bullet horizontally that they will fall at the same rate and hit the ground at the same time. somehow I don't believe this. if this is true how can a bullet travel hundreds of yards? can anyone explain this to me.

I dont believe it either but how hell ya gonna prove it

Gravity
 

Gravity is pulling both bullets down at the same rate (assuming both bullets are the same). Both bullets should hit the ground at the same time, if the ground is level, and if the fired bullet was fired parallel to the ground. The difference in impact points is due to the explosive energy from the gun powder driving the fired bullet forward as it falls.

A bullet begins to fall the instant it leaves the muzzle. That's why the line of bore is higher than the line of sight. Where they cross is what the gun is sighted in for. However there are other things to consider. The main one is barrel rise due to recoil (especially in a handgun). But these are interior ballistics that effect things before the bullet exits the bore. Once its out, gravity takes over and is boss.

If both bullets are exactly the same. Say a .224" 50gr Hornady V-max. If you shoot a bullet and drop it at the same time yes they will hit the ground at the same time. Gravity is a constant and never changes on earth.

This would only prove true in a vacuum. Same as droping a lead weight and a feather. In a vacuum both will hit bottom at the same time.

Gravity
 

I can't think of any bearing that a vacuum would have on the rate of fall, unless by vacuum you just mean a lack unequal external forces acting on the bullets. Gravity is the determining factor here.

Doesn't need to be a vacuum. Gravity pulls the same no matter what just as others have said here.

Correct except line of bore is BELOW line of sight. Think about it: sights or scope on a gun (line of sight). Above or below the barrel?

Yes, you do need the vacuum. Air creates resistance that takes a greater effect on a lighter object. Don't believe me? Drop a piece of paper and a rock at the same time. The air resistance restricts the paper's fall. In a vacuum, there is no air so the resistance isn't there.

Also, a bullet actually arcs upwards as it leaves the muzzle. That bullet would have a further distance to fall, so would probably hit the ground last.