wasnt that hard? Contains a slight mistake though. The speed of light is not relative. Everything else is relative. The speed of light is a constant.
I don't see how the answer is 1 instead of 100, so wany3, would you mind explaining why my reasoning is wrong real quick?
If you have two ships going at 99% of the speed of light and one fires laser, the photons shoot out at 100% (obviously). The first ships keeps moving at 99% of the speed of light, so you need to see where the photon and the ship intersect on a one-dimensional linear axis, as they're going in a straight line. So you'd do:
1 + .99x = x
Where 1 is the 1 light year head start the ship has, .99 is the length in lightyears the ship travels in a year, and x is the number of years (so the right side should be thought of as 1x, as the laser is going 1 lightyear/year, at the speed of light). Then you'd just solve it easily and get x=100.
Or to think of it in a different way, the laser would reach where the target ship was at the very moment it was fired in 1 year. However, since the ships are still moving, the ship would be .99 lightyear further at that point... so that would cyclically repeat by subtracting .01 each time until the difference finally reaches 0, which would take 100 years.
To get the answer of 1, you'd have to be thinking in terms of the two ships as the frame of reference, as if they weren't moving, and the photon moving between them. If this was shooting a cannonball or something I'd see it would be 1 year, as the ball's speed could increase to the speed of the ship + the speed gained by being shot out. However, in this case, for the answer to be 1 year, wouldn't the laser have to be going at the speed of light relative to the two ships PLUS the speed of light that lets it travel the distance in one year, so really 1.99 the speed of light? Which obviously isn't possible as the light always travels at the same speed...
