When you fire a gun into the air does the bullet return to earth at the same velocity that it left the barrel of the gun?
No. The only force pulling the bullet down is gravity. It will accelerate from whatever height at which it stops at 9.8m/s[sup]2[/sup] until it reaches its terminal velocity or hits the ground.
To clarify friedo’s answer a bit… In a vacuum, the answer would be yes. Since the height of the bullet is determined by how much gravity decelerates it, gravity would accelerate the bullet the same amount on the return trip, thus making the speeds equal. Since we don’t live in a vacuum, though, it won’t.
First of all, wind resistance will slow the bullet faster, so it won’t go as high as it needs to in order to accelerate back to its original speed.
Second, on the way down, the bullet will reach terminal velocity (or hit the ground) well before it reaches the speed it was fired at.
Jman
This one has been done a few times before
Can a bullet fired into the air kill someone when it comes down?
and the conclusion was that you could be killed this way.
Russell
Thanks Jman, I should have clarified that in a vacuum it’s true. So in High School Physics, the answer is yes. 
But in the Real Worls, it’s no.