It seems clear, pointed, and of broad interest. I doubt most introductory students of physics could answer it without thought.
I've just added another (just second) negative vote to the original question once my suspicion was confirmed: It is not really a question, it is an attempt to promote obvious misconceptions about relativity.
Dmckee gave an answer (which I upvoted). Some of its general lessons are:
- One should discuss the energy-momentum vectors, not just "masses and velocities" to meaningfully describe collisions in relativity.
- The final motion of products of elastic collisions is determined from the dispersion relations; and from the energy-momentum conservation law.
- The rest masses of composite systems aren't additive as you demonstrably kept on assuming.
He also added technicalities but these three key observations should have been enough for you to try to refine your wrong "derivations". But you, Will, just ignored everything in the answer and continued to promote your misunderstandings. When I realized that you ignored the answer, my suspicion was confirmed and I downvoted your question.
I also downvoted your "answer" to your own question because it doesn't answer the original question what happens in the collision. The answers should answer the original question. When they don't, they may be reasonably downvoted, even if we ignore the "awkward" fact that the author of the answer and the author of the question are the same person.
Here on the meta-website, I downvoted your question because I find it absolutely unacceptable for users to complain about every single negative vote they receive, especially when it must be pretty much obvious to them that there are very good reasons to downvote these questions and answers. That's how spoiled brats, not constructive users of a questions-and-answers website, behave.
By these negative votes (for which I sacrifice -1 of my reputation, so it's not for free), I am giving the system some information which is service to the community, too. One of the reasons of the negative vote is that I want you to discourage from posting additional questions and answers to this server because I am gradually concluding that additional contributions of yours won't lead to anything positive.