An unstable high-energy particle is created during a collision in the Large Hadron Collider (LHC). Its speed relative to the stationary collider is measured to be 0.995c, and the particle leaves a track 12.05 mm long before it decays. (This distance is measured in the collider (laboratory) frame of reference.) a) How long does the particle exist for in the laboratory frame of reference? b) What is the proper lifetime of the particle? That is, how long would the particle have lasted before decay had it been at rest with respect to the LHC? c) How far did the particle travel in its own frame of reference? (In other words, what length of the LHC did the particle see pass by it before it decayed?)