Tau leptons are fundamental particles with a mass of 1777 MeV/c² and a mean lifetime of 2.903 × 10-¹3 s (as measured in the rest frame of the tau lepton). Imagine that a tau lepton is produced in a high energy collision, such that it has a kinetic energy of 6125 MeV as measured in the laboratory. Assuming that it survives for one mean lifetime in its own reference frame, what distance does its decay occur from the point where it was produced as measured in the laboratory (i.e. how far does it travel in the laboratory before decaying)?

Tau leptons are fundamental particles with a mass of 1777 MeV/c² and a mean lifetime of 2.903 × 10-¹3 s (as measured in the rest frame of the tau lepton). Imagine that a tau lepton is produced in a high energy collision, such that it has a kinetic energy of 6125 MeV as measured in the laboratory. Assuming that it survives for one mean lifetime in its own reference frame, what distance does its decay occur from the point where it was produced as measured in the laboratory (i.e. how far does it travel in the laboratory before decaying)?