Question

A moving Lab A is moving with a velocity v=0.9c in relation to lab B, in the direction of the positive x axis. Particle kis at rest in Lab A. At one point the particle k splits into two particles, both have the same mass, MeV 140 and each has the rest mass of c . Each one of these particles moves at velocity V1 = 0.6c in relation to lab A: One of them, at, moves in the positive direction. After 30 nano seconds (the time is measured in the system in which the particle is at rest), the particle a decays. What is the time that is measured in Lab A, from the moment of the original split of k until the particle at decays?

Answer 1

We want to measure the lifetime of π⁺ in Lab A. π⁺ is moving at speed 0.6c in lab A. Due to time dilation as a result of this relative motion, the lifetime of π⁺ will be longer in lab A. The lifetime of π⁺ in lab A is

이들 I

T_{​​​​​​o} is the lifetime of π⁺ in its rest frame.

Substituting

T. = 30 ns, v1 = 0.6 C

T=- 30 ns 1 - (0.6 c)2/c2

T = 30 ns 1 -0.36

T = 37.5 ns