I understand that nothing can move faster than light due to time dilation. I want to build upon my understanding of Einstein's theory of Special Relativity, so I came up with this hypothetical problem for myself:
If both particles are moving at 0.9c towards each other (according to an observer on Earth), what speed does each particle have relative to the other?
I'm stumped since I am only familiar with Newtonian classical mechanics to solve this (which would be wrong).
I am aware of Lorentz' factor $\gamma =\frac{1}{\sqrt{1 - \frac{v^2}{c^2}}}$ and the time dilation equation $t_m = \frac{t_o}{\sqrt{1 - \frac{v^2}{c^2}}}$, but I'm not sure how to apply it in this instance. I'm just looking for a gentle push in the right direction.
Edit: My prior research:
This article, https://what-if.xkcd.com/1/, talks about the effect of a baseball thrown at 0.9c would have as it traveled towards a batter. This is not what I'm looking for since it doesn't explain the math behind finding the collision speed between two high velocity entities.
This question on Yahoo, https://answers.yahoo.com/question/index?qid=20110529201519AAxbxvm, asks a similar question to mine, but no math is involved to demonstrate the calculations behind the reasoning.
This question on Physics.SE, Collision between a photon and a massive particle, does not answer my question either. I have not been able to find a similar Physics.SE question which can provide me to clues to my own hypothetical question.
I have also Googled the following phrases:
i. "collision faster than the speed of light"
ii. "collision of high speed particles"
iii. "lorentz transformation in a collision"
iv. "collision analysis at light speed"