I hope you have heard of a physics situation like this: "A bullet is fired inside a train that is moving forward and another bullet is fired outside from ground." It is simple that one fired from inside the train will be faster and reach a common target before the other. What if it is repeated in space. Assume that no recoil happens and the train is also vacuum inside i.e. no air inside or outside the train. Further assume that train started moving forward after the bullet was fired.

I know that both should reach a common target simultaneously now, just want to confirm.

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    $\begingroup$ No, I haven't heard of this one before, but if I understand you correctly (meaning, there's no effects of aerodynamic drag taken into account either way) then there's no difference between the two scenarios. However, it almost sounds like the second case is different, in that the train only starts moving after the bullet has been fired. If that is so, then, yes, that train is there purely for decoration and does not affect the physics so, yes, both bullets will reach the target at the same time. Again, the way I understand the assumptions made, the presence or not of a vacuum is irrelevant. $\endgroup$ – Pirx Nov 26 '16 at 22:44
  • $\begingroup$ Yes, you understand me correct. However i think that having a vacuum inside the train is also necessary...i dont really know how or why...just feel that moving walls of train will push the air which will in turn push the bullet giving it a boost in velocity...its my thinking.. $\endgroup$ – Gaurav Goyal Nov 26 '16 at 22:50
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    $\begingroup$ Sure, if you take into account aerodynamic drag, then the presence of air does make a difference, but it is going to be tiny. $\endgroup$ – Pirx Nov 26 '16 at 22:58
  • $\begingroup$ If in one case the train is moving when the bullet is fired, and in the other case it is stationary when the bullet is fired, then the 2 situations are not equivalent. This is the significant difference, rather than whether the experiment is performed in space or on Earth. $\endgroup$ – sammy gerbil Nov 27 '16 at 0:05
  • $\begingroup$ Satellite deployments in orbit actually represent the same physics and are done in vacuum. $\endgroup$ – dmckee Nov 27 '16 at 0:09

What's important in this scenario isn't whether there is air in the train or not, but whether the bullet (and, presumably, the gun that fires it) has any momentum before the gun is fired. The action of firing the gun exerts some impules $\Delta \vec p$ on the bullet, but its final momentum depends on its initial momentum.

For example, sometimes on long car rides my children think it's amusing to toss paper airplanes from the back seat to the front seat. On the ground, my children can toss paper airplanes at perhaps five miles per hour. If I'm on the highway, someone on the side of the road might measure a backseat-to-frontseat airplane as having a speed of seventy-five miles per hour. That's not an effect of the air in the car (and believe me, I've imagined removing all the air from my car on some of these trips); it's an effect of the initial momentum of the airplane.

You usually hear about this "puzzle" when one of the velocities is close to the speed of light. For example, if $u$ is the speed of the car/train and $v$ is the speed of the paper airplane/bullet after it's thrown/fired, the observed speed after the toss/shot is always given by relativistic velocity addition: $$ \begin{align} v' &= \frac{u + v}{1 + \frac{uv}{c^2}} & &(\text{always}) \\ &\approx (u+v)\left( 1 - \frac{uv}{c^2} + \cdots \right) & &\left(\text{if } \frac{uv}{c^2} \ll 1\right) \end{align} $$

For a bullet (say, $v\sim 300\rm\,m/s$) on a train (maybe $u\sim30\rm\,m/s$) the difference between the "right" way and the naïve way $v'=u+v$ starts somewhere around the thirteenth decimal place, which is pretty deep in "don't care" territory: if the gun is the same, a bullet fired forwards from a moving gun will move faster than bullet fired from a stationary gun.

  • $\begingroup$ There is no initial momentum. I mentioned in the question that train started moving after the bullet was fired. $\endgroup$ – Gaurav Goyal Nov 26 '16 at 23:58
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    $\begingroup$ @GauravGoyal Currently (v3) the question states it both ways ("is moving forward" and "started moving after"). Hopefully this answer is clear enough in either scenario. $\endgroup$ – rob Nov 27 '16 at 0:01
  • $\begingroup$ as per for the 'air' part, here is a small experiment: next time on long rides, make two paper planes. Fly one from inside the car. For the other, lean out from the window and fly. In both the cases, the initial momentum is same, right? Why then the plane inside the car reaches from back seat to dashboard but the one flown from outside is swept back away from you...? $\endgroup$ – Gaurav Goyal Nov 27 '16 at 0:02
  • $\begingroup$ the 'is moving forward' relates to experiment on earth. I am not asking for the answer of that. The part of question which I asked answer for states "started moving after" $\endgroup$ – Gaurav Goyal Nov 27 '16 at 0:04

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