@tomsarbeck – I can see your point, they would both actually stay in the air for the same length of time. However, due to the rotation of the Earth, maybe one would cover a larger distance along the Earth’s surface than the other.
Some random thoughts in my head while listening to Repentless by Slayer.
If the Earth was to lose some of its mass as the bullet was fired, then it would travel further. If the bullet was fired from the gun with enough energy it would continue to travel in a straight line and leave the Earths’ atmosphere and keep going.
To think differently about the orbit of the moon, imagine that it is trying to travel in a straight line “away” from the Earth. However it is trapped in the curve of SpaceTime that the mass of the Earth has created. The moon is falling around the Earth just as the Earth is falling around the Sun. The mass of the moon is slowing the Earth’s rotation down (tidal friction) by a few milliseconds every century. The tidal bulge squashes the Earth and some to this energy is transferred to the moon (E=M). The moon is moving away from Earth at about 4cm per year which weakens the gravitational effect (less curvature of SpaceTime) they have on each other.
Back to the 2 bullets. They both fall towards the center of the Earth at the same rate of acceleration.
Another thought: if a photon of light leaves the Sun, traveling at 300,000 KM per second and you were to run after that particular photon at 299,999 KM per second, the photon of light would still be traveling away from you at 300,000 km per sec. For you to catch up with it you would need infinite energy to accelerate that last 1 km. That is “C squared” in Einstein’s equation. That is why nothing can travel faster than the speed of light.