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Curious Question about Velocity

  1. Oct 14, 2011 #1
    Can someone explain to me what will happen in this scenario?

    Imagine you are in a train which is travelling at velocity X. In it, you fired a gun which points towards the direction of the moving train launching the bullet out at the same velocity. Will this cause the bullet to travel at 2X? What if it was fired in the opposite direction?

    The important thing is not to stop questioning.
    Albert Einstein
  2. jcsd
  3. Oct 14, 2011 #2


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    You can already answer this yourself. Our earth is moving at a velocity X with respect to some other planet. And yes, we have fired MANY guns in many different directions already.

    So now ask yourself, how fast is the bullet moving with respect to you, on the earth, and with respect to another person on that other planet.

  4. Oct 14, 2011 #3
    I suppose that you mean that the velocity of the bullet determined with respect to the train, while the velocities X and 2X are determined with respect to the rails.

    In that case the bullet will travel at very nearly 2X; for all practical purposes you can take it to be 2X. However, at very great speeds, near to that of light, the difference becomes noticeable.

    As determined from the railway track, the measurement system of an incredible high speed train will be affected by the speed so that the bullet, although it looks like X as determined from the train, will add less than X to the speed of the train as seen from the railway track.

    In the opposite direction the effect is also opposite: the bullet's speed will subtract with very slightly more than X from the speed of the train as determined from the railway track. For trains and bullets and usual requirements of precision, the the bullet's speed will be X-X=0.

    If you want to deepen your understanding for very high speeds (or extreme precision), please ask for details in the relativity forum.
    Last edited: Oct 14, 2011
  5. Oct 14, 2011 #4
    Well bullets are generally much faster than trains, so the bullet's velocity is going to be more than 2x. But basically, the velocity of the train will be directly added to the velocity of the bullet (or subtracted, if fired in the opposite direction). If the bullet is indeed just as fast as the train, then its velocity relative tot he ground will be 2x.

    This is generally true until you start getting near the speed of light, but we needn't worry about that at everyday speeds.
  6. Oct 14, 2011 #5
    Interesting, doesn't it also mean a person standing on the ground (train station) will see the bullet is hanging at one point in the air, not moving?
    Even though the bullet is moving, the 'inertia speed' of the bullet will cancel the 'firing speed' of the bullet, as a result the bullet will appear to be hanging at one point in space. I can't even imagine this situation. Of course, all external disturbances must be eliminated.
  7. Oct 14, 2011 #6
    As Lsos pointed out, a normal bullet goes much faster than a normal train. But yes, launch a projectile backwards out of a train with the same speed as the train is going, and it will fall straight down with respect to the ground.
  8. Oct 14, 2011 #7
    ...and curiously the gun will still kick the same due to the force needed to "stop" bullet from going the speed of the train. :smile:
    Last edited: Oct 14, 2011
  9. Oct 14, 2011 #8


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    On the contrary, it is not hard to imagine at all. In fact it is quite mundane.

    The bullet does not hang at all, but falls to the Earth exactly as if someone was standing next to the rail and dropped it from their hand.

    When you fire a gun horizontal to the Earth, the bullet, despite travelling at Mach speeds (or in your special case, only as fast as the train) falls to the ground exactly as if it is not moving at all. The X-component of its movement has no effect on the Y-component of its movement.

    Mythbusters demonstrated this by firing a gun and dropping a stationary bullet simultaneously. They hit the ground simultaneously.
    Last edited: Oct 14, 2011
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