In a laboratory experiment a muon is observed to travel 800

In a laboratory experiment, a muon is observed to travel 800 m before disintegrating. A graduate student looks up the lifetime of a muon (T = 2 x 10^-6s) and concludes that the muon\'s speed was u = 800m/2 x 10^-6s = 4 x 10^8 m/s. Faster than light! Identify the student\'s error, and find the actual speed of this muon.

Solution

u = c / sqrt [1 + c² T² / l²]

v = c / sqrt [1 + (3 * 10⁸)² (2 * 10^-6)² / 800²]

v = (3 * 10⁸) / 1.25

= 240000000 m/s

= 2.4 * 10⁸ m/s