2. Two protons collide head-on at the Large Hadron Collider (LHC), each travelling with a relativistic velocity, the same for the two protons. A proton's weight is about 1GeV/c2. (a) The collision produces a single unstable particle whose mass is 130GeV/c2, somewhat larger than the Higgs boson (125GeV/c2). What was the protons' y-factor and how fast were they moving? (b) The unstable particle decays into the Higgs boson (125Gev/c2) and two protons. Is it possible for the Higgs boson to be ejected with speed 0.6c? (c) Instead, the unstable particle decays into two hypothetical proton-like particles, each with a rest mass of 50GeV/c2. How fast are these two hypothetical particles moving? (d) At the real LHC, the y-factor for the protons is about 7500. If the two protons were to produce a single unstable particle when colliding, what would this particle's mass be