Answer to Question #135769 in Mechanics | Relativity for Marciales nicole

Question

A particle is observed to have a lifetime of 1.50 X 10^-6 s when it is at rest in the laboratory. What is its lifetime when it is moving at 0.800c? How far will the particle move with respect to the moving frame of reference before it decays? How far will the particle move with respect to the laboratory frame before it decays?

Answer 1

Solution

Lifetime in moving frame is given by

$t'=\frac{t}{\sqrt{1-\frac{v^2}{c^2}}}$

$t'=\frac{1.50\times10^{-6}}{\sqrt{1-\frac{(0.800c)^2}{c^2}}}$

$t'=2.5\times 10^{-6} s$

distance travelled by particle before decays is

$d=v\times t'=0.800c\times2.5\times10^{-6} \\ d=600 m$