Answer to Question #88924 in Mechanics | Relativity for Sridhar

Question

The lifetime of π-mesons is 2.5×10^-8 and their speed is 2.7×10^8m/s the distance travelled by π-mesons as seen by the observer on the earth during their lifetime is

Answer 1

The lifetime of π-mesons for the observer on the earth is

$$t=\frac{t0}{\sqrt{(1-\frac{v^2}{c^2})}}$$

where t0 - lifetime of π-mesons;

v - speed of π-mesons;

c - speed of light.

The distance travelled by π-mesons as seen by the observer on the earth during their lifetime is

$$l=v\times{t}=\frac{v\times{t0}}{\sqrt{(1-\frac{v^2}{c^2})}}=21.35 m$$