How to deduce the theorem of addition of velocities?
Let's say that you are in a rocket speeding at 90% the speed of light away from Earth. Now fire a bullet inside the rocket that is also going at 90% the speed of light. According to Newtonian physics, we add both velocities. Thus, the bullet should be going at 180% the speed of light.
But we now know that according to Einstein the sum of these velocities is actually close to 99% the speed of light, because length contracts and time slows down.
But how can you determine mathematically, that bullet is going at 99% the speed of light?
Additionally, can you also calculate, how much time is slowed down, if you know the velocity? Is there any formula?