An electron is accelerated through a potential of 10^9V to the right. A proton is heading to the left towards the electron at .9c.
Find E,K,p for the electron and proton from the rest frame, and from each others frames.
The Attempt at a Solution
Since the potential is 10^9V, the kinetic energy of the electron is K=10,000MeV, and the rest mass is mc^2=.51099MeV. So E=10000.51 MeV.
Using E=γmc^2, I get γ=19570.9, and β=.999999999
Which gives me values of E=10000.53 MeV, K=10000.02 MeV, and p=E/c=10000.53 MeV/c.
For the proton, I do similar math to get E=2152MeV, K=1212.3 MeV and p=2152 MeV/c.
Now to find the E,K,p of the electron from the reference from of the PROTON, I use the combination of velocities equation u'=-ve-vp/(1+vevp/c^2) and I always get the speed of the electron u'=c. How do I get around this? if u=c, then λ=∞, and all the energies and momenta are infinite.. :( Am I doing something wrong? :(