Is it possible to have a floating bullet in the air? I've been asking myself a question for quite some time :


*

*say that a bullet gets out of a gun at 900 km/h (I'm european, hence the metric system).

*say a train could go in a straight line at 900 km/h

*say you're at the back of that train, and you'd shoot a bullet backwards. The bullet exits your gun at 900km/h and flies away from the train at the same speed.
However, what would happen for an earth observer?


You'll agree that if you shoot in an open field, the bullet will stay at the same altitude for several seconds before falling to the ground (with a field large enough).
So from that train, same thing applies.
So for the earth observer, the bullet will not have an horizontal speed, and will stay at the same altitude for several seconds before falling to the ground.
So basically it'll float up in the air without falling. That'd be strange for the earth observer, right?
But the horizontal speed will decrease of course.
So for the earth observer, the bullet will, for a few seconds, stay still at the same position, and then after several seconds will start to fall down a little bit, and will start to move towards the train, because its horizontal speed towards the train will decrease. Strange again!
OK last one: what would happen if the earth observer tried to catch the bullet with his bare hands? Nothing right? Just maybe a very hot bullet because of the explosion but it'd be basically as easy to catch as a stone floating up in the air?
And don't tell me that the bullet will slow down due to air friction, because remember the bullet is not moving. Or very slowly.
 A: You are standing at the back of the train, facing backwards. The train, you, the pistol in your hand and the bullet inside the pistol are all travelling at 900 KPH from the point of view of a track-side observer. However, in your frame of reference, all those are stationary but the landscape, surrounding air and the observer are all moving at -900 KPH.
As you pass an observer, you pull the trigger, the exploding charge in the cartridge accelerates the bullet.
In your frame of reference you see the bullet accelerate from 0 to -900 kph.
In the observer's frame of reference she sees your bullet decelerate from 900 kph to 0
If the observer drops a bullet from her hand as you pass, she, and you, will see the bullets follow the exact same trajectory.
She will see both bullets fall down to the ground from 0 kph (vertically) accelerated by gravity (less air resistance). The two bullets will reach the ground at the same time.
You will see the observer and both bullets travelling away from you at -900 KPH. Both bullets will follow a parabolic path away from you (in your frame of reference).
The maths isn't difficult. If you are not convinced, try drawing a diagram and working the calculations from both frames of reference. 
A: Even given the conditions that you're indicating, the bullet would most certainly not hover in the air. It would immediately begin falling to the ground as soon as it left the barrel.
Horizontal velocity has absolutely no bearing on vertical velocity, and if you're discounting wind in this example, which I'm assuming you are based on the premise of a stationary bullet, then you would have no aerodynamic effects acting on the bullet, hence no floating.
A: 
"You'll agree that if you shoot in an open field, the bullet will stay at the same altitude for several seconds

No, we wouldn't. 
In fact we do a demo (often called 'shoot the monkey') in introductory classes that shows unambiguously that it falls very much as if you had held it at arms length and dropped it. As noted in the comments the Mythbusters guys actually ran the experiment with a bullet.
