Two protons are moving away from each other. In the frame of each proton, the other proton has a speed of .555c.[In the rest frame of the earth the protons are moving in the opposite directions with equal values of speed. What does an observer in the rest frame of the earth measure for the speed of each proton? Enter your answers numerically separated by a comma I thought I would just divide by 2.... clearly it is wrong. The answer is .303c, after failing many tries on mastering physics. I want to know how you do this problem. Thank you.
Your problem is that you assumed "Galilean Relativity" where velocities add directly. For higher speeds this line of thinking fails. Velocities dont add directly, they add in a weird way. You should have some formula for this in your notes or text, something along the line of "velocity addition". A key thing to realize here is that since we have high speed objects we cannot add velocities directly. Intuitively we think that velocities add directly and this is confirmed by our experience with "slow" objects (slow being up to jet speed and beyond...). But when you have higher speed objects you need to stop trusting your intuition and look at the theory, the theory of relativity. So one thing you want to ask yourself whenever you see problems like this, ask "Is this relativistic?". If not, proceed with your intuitively understood kinematic equations. If it is relativistic you need to consider the equations of relativity.