Lissajoux
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Homework Statement
An electron e^{-} and a positron e^{+}, each with a total energy of exactly 5000 MeV, collide head-on and annihilate to produce a tauon/anti-tauon pair, \tau^{-} and \tau^{+}, and no other particles.
1. For the electron moving before the collision, state or calculate the mass energy of the electron, in MeV.
2. Show that the \tau^{-} and \tau^{+} move in exactly opposite directions with equal magnitudes of momentum.
3. Assuming that the \tau^{-} and \tau^{+} have exactly equal masses, what is the total energy of each?
4. If \tau^{-} and \tau^{+} both have momentum of magnitude 4675 MeV/c, estimate the tauon mass.
Homework Equations
Within the problem statement and solution attempt.
The Attempt at a Solution
1. Is this just 5000 MeV? or do I use:
E=mc^{2}\implies m_{e}=\frac{E}{c^{2}}
I thought that it's the value stated in the question, but that seemed too easy, but this other method gives messed up units. Maybe there's another way, or I was correct first time.
2. I'm not sure how to do this at all

3. Again, not sure how to do this. Sure it's not a tricky calculation though.
Perhaps conservation of energy and conservation of momentum are playing their part in these 2 questions.
4. Expression for momentum is P=mv so I just need to rearrange the equation, and find out the velocity of the tauon. Not sure how to calculate this. Unless they are moving at v=c, that's just a thought.
.. SO I don't think I'm too far from the answers, hopefully getting the right ideas, just could do with some advice on the tricky bits.
