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If I'm running at say $400\: \mathrm{m/s}$ and a bullet travels at $400\: \mathrm{m/s}$ and I fire the gun, will I see the bullet leave the barrel?

I either see it stay in the barrel floating because we are moving at the same speed. -- Or -- The bullet would move and have a speed of $800\: \mathrm{m/s}$.

What is the correct answer?

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  • $\begingroup$ Initially it would go at 800 m/s, since the exit speed is relative to the gun. $\endgroup$ – ja72 Dec 11 '13 at 21:57
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    $\begingroup$ Which direction are you running? How is the barrel oriented? $\endgroup$ – BMS Dec 11 '13 at 23:27
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At low velocities like this you can ignore special relativity and simply add the two velocities. This is really easy to see if you imagine yourself standing still and the Earth moving under you. Relative to you the gun should fire just like you were standing still. This is called an inertial frame of reference.

You see the bullet leave at $400\: \mathrm{m/s}$ (relative to you) and the Earth sees the bullet leave at $800\: \mathrm{m/s}$.

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  • $\begingroup$ I should mention that this is the case because the bullet is "pushing" off of the gun. If the bullet were somehow pushing off of the air around you then the air rushing around you at $-400\: \mathrm{m/s}$ would prevent the bullet from zooming away from you. $\endgroup$ – Brandon Enright Dec 11 '13 at 20:47
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    $\begingroup$ It should be made clear that you will always see the bullet leaving your gun at 400 m/s no matter how fast you are going. Special relativity only predicts a difference in the speed people standing still see the bullet move. $\endgroup$ – Brian Moths Dec 11 '13 at 23:16
  • $\begingroup$ @NowIGetToLearnWhatAHeadIs absolutely. In the reference frame of the Earth though it won't always be $400\: \mathrm{m/s}$ more than the velocity of the shooter (due to relativistic effects). $\endgroup$ – Brandon Enright Dec 11 '13 at 23:25
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because a bullet does not travel at a constant speed, it would most likely shoot ahead of you (more than 400 m/s) but than even out with you untill there is a change in velocity. (this is just a theory from me, and i have no education in the field of physics, im in 9th grade)

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  • $\begingroup$ neglecting air resistance and gravity, the bullet would indeed travel with a constant velocity. $\endgroup$ – Astrum Dec 11 '13 at 20:58
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At the point the bullet leaves the gun it is traveling 800m/s.

You need gravity to run; I guess he could be running in a vacuum.

This is with random values. You would have to construct a bullet decription for yourself in a Ballistic Calculator.

To see how long the bullet will keep up with you, consult a ballisticCalculator

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  • $\begingroup$ Also, in the Calculator, the initial m/s should be set to 800m/s. $\endgroup$ – user35686 Dec 11 '13 at 22:57
  • $\begingroup$ This is to show how long the bullet would keep up, if you ran at 400m/s. I lost some text in my post I guess. $\endgroup$ – user35686 Dec 13 '13 at 0:08

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