We all know about the ultimate speed limit... the speed of light.

If person A stands on Earth and shoots his pistol, he observes the bullet to fly directly away at 1000 mph. Person B is standing right next to him (not in front) and watches this event, and agrees that the bullet flies directly away at 1000 mph.

Let's change the situation and say that B is in a spaceship, and A is in a different (and very long) spaceship with lots of windows. B's ship is hovering in space (no thrusters/acceleration). A's ship is approaching from a distance and is going to pass B's ship (very close) but at incredible speed. Make careful note that A's ship is NOT thrusting or accelerating at all, it is "coasting". In fact, A's ship is moving, relative to B's ship at 10 mph less than the speed of light. WOW!

A stands in the middle of his ship and points his gun directly forward (in the direction of travel), and fires the same pistol at the exact moment that he is passing B.

The questions are: How fast does he observe the bullet leave the gun? How fast does B observe the bullet leave the gun?

How do your answers change (if at all) if A aims backwards when he fires?

(In reply to What a doppler effect! by Eric)

Okay,

I recognize that there will be a difference in apparent speed of the bullet should the gun be fired in the negative x direction rather than the positive by the mini-doppler effect of the bullet itself. Now we will be working with REALLY small speeds. Since the bullet fired in the negative x direction is leaving B apparently slower than A is leaving B the doppler effect will detract from A's apparent speed more than it will detract from the bullet's apparent speed. More clearly, at time t = 2 (or so) A will be at x = 1 light-hour (or so) and the bullet will be at 1 light-hour - 1/60 thousandth of a mile (about 1 inch closer to B than A is). When B sees this inch seperation though, B will be seeing A before the bullet had spanned the inch making the bullet seem to be travelling even slower relative to A but not as slow as it would seem were the bullet fired away from B. Either way we are looking at speed differences way too small for me to figure. I hope someone else has fun with this one.

Posted by Eric on 2003-11-28 21:59:53