Do a fired bullet and dropped bullet reach the ground at the same time?

[eric.rumery]

If you are standing atop a 2 story building and fire a bullet vertically towards the ground and drop one from the same height will they arrive at the same time? I am not a physics person but my girlfriend is in it now and tells me that they would arrive at the same time. I don't see this to be true due to the second force acting upon the fired bullet. Can someone please explain this to me in lamens terms. I believe the fired bullet rotate on an axis increasing its terminal velocity anyway?
Thank You,
Eric

 

[rcgldr]

If you are standing atop a 2 story building and fire a bullet vertically towards the ground and drop one from the same height will they arrive at the same time? I am not a physics person but my girlfriend is in it now and tells me that they would arrive at the same time. I don't see this to be true due to the second force acting upon the fired bullet. Can someone please explain this to me in lamens terms. I believe the fired bullet rotate on an axis increasing its terminal velocity anyway?

You need to clean up the wording here, the bulled is fired horizontally, and the other bullet dropped at the same time the first bullet leaves the barrel. With no atmoshpere, and a relatively flat earth, both bullets land at the same time.

With an atmosphere, the fired bullet will take a bit longer to fall than it would without an atmosphere, but so would the bullet dropped. I suspect if the bullet dropped started tumbling (rotating at a high rate), it would hit the ground later.

Ignoring the overly techinical stuff, the point here is that horizontal motion doesn't affect the vertical motion.