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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.

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This question has two false statements (that the bullet magically hangs without falling and that there's zero air resistance on it) that are immediately followed by statements that you refuse to hear disagreement on these points. This hardly entices me to help you understand the situation better. –  Mark Eichenlaub Nov 9 '12 at 22:32
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Regarding catching the bullet, it has been done. I believe it was some pilot who just stuck his hand out to catch something in air, only to later find out that it was a bullet shot at him from an enemy aircraft. since he was wearing gloves, he did not burn his hand. Found a link. –  mythealias Nov 9 '12 at 22:44
    
The question can be framed better, but I don't see why down vote it. –  mythealias Nov 9 '12 at 22:47
    
@mythealias: that is a very cool story! Thanks a lot for this link –  Benoit Duffez Nov 10 '12 at 9:13
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3 Answers

up vote 13 down vote accepted

"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.

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I thought we would. I thought that the trajectory of the bullet would be parabolic, and that the bullet would vertically fall in a slower motion than if it was dropped from hand. Bad assumption I guess! thanks for your answer. –  Benoit Duffez Nov 10 '12 at 9:17
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@Bicou That is actually a very common thought coming into a intro course, and one of my personal goals when teaching projectile motion is to get students to convince themselves. May I ask if you found the video convincing? Or was there something else? –  dmckee Nov 10 '12 at 15:27
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I liked the video, however the starting angle is above the horizon, so the trajectory is an arc. I think it would be clearer with an horizontal shooting angle. And what would be really PERFECT would be a slow motion of the bullet for all its trajectory. I guess it's not possible or way too complicated. The really best would be to see the trajectory from behind, so the horizontal speed would not be noticeable (except from the fact that the bullet will get smaller because it'd get farther). On the side drop a bullet from your bare hand, and see that both hit the ground at the same time. –  Benoit Duffez Nov 10 '12 at 16:49
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Also the American TV show MythBusters did an interesting segment where they (after a lot of experimentation) fired a bullet and at the same time (as close as they could manage) dropped a bullet from a position down range where they expected the fired bullet to impact. The two projectiles hit the floor within, I think, a thousandth of a second of each other. –  David Rouse Nov 10 '12 at 20:12
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That is a f.. awesome video! Found it here: youtube.com/watch?v=D9wQVIEdKh8 Thanks a LOT David! I've been wondering this for ages :) (@dmckee maybe you could add it to your answer?) –  Benoit Duffez Nov 11 '12 at 18:31
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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.

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Yeah that was basically my mistake here, I thought that the big horizontal velocity had an impact on the vertical one, it turns out it doesn't, of course. –  Benoit Duffez Nov 10 '12 at 9:25
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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.

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I certainly could accept your answer as well, because it explains basically the same thing. Thank you for your answer! –  Benoit Duffez Nov 10 '12 at 9:30
    
One addition: in the frame of reference of the person standing at the back of the train, the air is close to motionless. To the observer on the ground, there is a nearly 900KPH wind (caused by the train passing) in the direction of the train. This would slow the bullet down relative to the shooter, causing it to move towards to train relative to the ground observer. –  Michael Jun 17 '13 at 14:32
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