Suppose you're traveling on a space ship at 9/10 the speed of light (.9c). You have a high-powered rifle that shoots bullets at the same speed. Suppose you shoot the bullet perpendicular to your direction of travel.
It appears that the bullet would travel at a 45-degree angle (northeast, if the ship is traveling north and the bullet is shot eastward), at about 1.2728c which is faster than light. Why is this wrong, and what would the actual speed and direction be?
(In reply to
First thoughts. by TomM)
To clarify the difference between speed and velocity: Velocity is just speed with a direction attached. Velocity is a vector quantity, whereas speed is simply a scalar (just the rate of movement without any particular direction specified). This is true whether you're speaking in terms of classical or relativistic terms. (Note that c is the "speed of light" not the "velocity of light".)
So, in my original problem you may assign any direction you like to the .9c speed, and use that as a velocity--the problem will be the same (which you did), but that's not necessary to solve the problem. Nonetheless, you definitely do have to think in terms of speed and direction (ie, vectors) to solve this.
The point you make about what the speed is relative to (which is a valid point), would also apply whether we're speaking in classical or relativistic terms. But pick any reference frame to be the at-rest frame (you chose some planet, which is fine), and solve from there. We don't need to specify what the at-rest frame is in order to understand and solve it.
I'll wait for more answers before I post the solution--you're on the right track, but not quite there.
Edited on January 18, 2005, 5:37 am
re: First thoughts.
