Who has been on a bullet train?

If a person (shooter) is standing at point A, and a train is running on a track at point B to C (the width of the train), if the person at A shoots at the train, how does the track of the bullet change (if at all) once it enters the moving train?

• Does relativity come into affect at all? Would the path of the bullet follow the original path or "bend" ever so slightly to accomodate the (hypothetical) acceleration of the inside of the train? I apologize in advance if this isn't clear enough.

• Answer:

  Newton's first law is [math]F=ma[/math]; that is, Force equals Mass times Acceleration. If there is no force on the bullet, then there is no acceleration. Unless the bullet hits something on the train, or we try to take wind resistance into account, there's no force, so no acceleration. There is actually an older kind of relativity at work here, called Galilean relativity. That relativity states that people in different reference frames will observe objects moving at different speeds. There are three reference frames here: that of the bullet, that of the person with the gun, and that of the train.  To the guy firing the gun, the bullet appears to be moving very fast, but to the bullet itself, the bullet itself is standing still but the guy with the gun is moving backwards very fast. A person on the train has a third perspective of both of those. The differences between these reference frames are handled fairly easily. The velocity (speed and direction) of each reference frame can be represented by a vector, and you add or subtract vectors to calculate what things must appear like to somebody in a different reference frame. ( gives an excellent description of the basic math there.) It's important to note that that's just a calculation, to change from one set of coordinates. Newton's Laws apply only within a reference frame. The calculations to change from frame to frame are not a real acceleration, so no force needs to be applied. In other words, we can change our perspective from the person's to the bullet's to the train's, but it's only our perspective that's changing, not the velocity of any real object.The bullet itself isn't being accelerated just because it moves inside the train. From the bullet's own point of view, the existence of a different frame of reference is irrelevant. That's good, because it means we don't have to figure out what it means to be "inside the train": the bullet moves exactly the same way before it goes through an open window as after. It would be very confusing if the window were so big that that it became a flatcar, and there wasn't any "inside" any more! Fortunately, that a problem for train builders, not physics or the bullet, which doesn't draw a distinction between "inside" and "outside". Now, there's also Einstein's relativity, and trains come up all the time there as examples. (So do rocket ships and elevators: anything that can move in a straight line.)  But unless you're moving near the speed of light, Einstein's relativity doesn't come into it. In Galilean relativity, you get from one reference frame just by adding up vectors. In Einstein's relativity, there's a peculiarity: the speed of light is the same in all reference frames. That wreaks havoc on the math: you can't add or subtract from the speed of light because it must always be the same. It turns out that you have to tweak the rules, and "addition" becomes a more complicated operation. Not too complicated, actually, but enough math that it goes beyond the scope of this question. Suffice it to say that there's a correction factor involved, involving the ratio of the speed of the object in the reference frame to the speed of light, and that's going to be essentially zero for any speed you're likely to encounter. When you set it to exactly zero, the math is precisely the same as in Galilean relativity.