Question

Observer A, who is at rest in the laboratory, is studying a particle that is moving through the laboratory at a speed of v=0.8c and determines its lifetime to be τA=129 ns. Observer A places markers in the laboratory at the locations where the particle is produced and where it decays. How far apart are those markers in the laboratory?

Answer 1

30.96 m

Step-by-step explanation:

If the particle has a lifetime of 129 ns as measured by observer A, and has a speed of 0.8c as measured by observer A, the distance between the markers will be:

d = v * Δt

v = 0.8*c = 0.8 * 3e8 = 2.4e8

Δt = ζ = 129 ns = 1.29e-7 s

d = 2.4e8 * 1.29e-7 = 30.96 m

This is the distance as measured by observer A.