Chapter 37, problem 001 the mean lifetime of certain subatomic particles is measured to be 2.7196 μs when they are stationary. however, the mean lifetime of fast-moving particles of the same kind observed in a burst of cosmic rays is measured to be 17.258 μs. what is the speed parameter β of these cosmic-ray particles relative to earth?

 v = 0.9875 c

Explanation:

This is an exercise of time dilation in special relativity, which is described by the equation

      t =  γ

      γ = 1 / √ (1 — v² / c²)

The most important is to find respect for which system the measurement is performed.

Since the particle is still, the measured time is the proper time = 2.7196 10-6 s, in the system where the particles move t = 17,258 10-6 s

Let's clear dam

     γ = t /

     γ = 17,258 10-6 / 2.7196 10-6

     γ = 6.345

     γ = 1 / √ (1-β²)

     1-β² = 1 /γ²

    β = √ (1- 1 / γ²)

    β = √ (1 - 1 / 6,345²)

    β = 0.9875

    v / c = 0.9875

    v = 0.9875 c

i had this question and the answer was 3.15 miles.

martina travels from school to her mom's office. from there, she walks to school. after school, she walks to the library and then to a friends house before finally ending back at home. find martina's total distance traveled.

a) 0 miles  

b) 0.4 miles  

c) 1 mile  

d) 3.15 miles