- #1
jethomas3182
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Homework Statement
From: http://www.phas.ubc.ca/~mcmillan/rqpdfs/1_relativity.pdf
The average lifetime of a pi meson in its own frame of reference is 26.0 ns. (This is its proper lifetime.)
If the pi meson moves with speed 0.95c with respect to the Earth, what is its lifetime as measured by an
observer at rest on Earth?
What is the average distance it travels before decaying as measured by an observer at rest on Earth?
Homework Equations
T=26 ns
v=.95c
t^2=T^2 + x^2
x=vt
The Attempt at a Solution
t^2 = T^2 + (vt)^2
t^2(1-v^2) = T^2
t^2(1-.95^2) = 26^2
t*sqrt(1-.95^2)=26
t=26/sqrt(1-.95^2) = 83.267 ns rounded to 83.3 ns Books answer: 83.3 ns
distance: x = vt = 83.3ns * 3*10^8 m/s = 24.99 m rounded to 25.0 Book's answer: 24.0
My answer is about 4% off.
83.267*.3=24.98
83.267*.29979=24.8
I got the median speed, but with halflife the median is mean*ln(2).
83.267*.29979/ln(2)=35.786 rounded to 35.8. Even worse.
Did the book make a typo, or am I missing something important?