Answer to Question #285674 in Mechanics | Relativity for Amos baite

Question

What is the velocity o π- meson whose proper means life time is 2.5× 10⅞ second

Answer 1

We know that

$\tau=\frac{\tau_0}{\sqrt{(1-\frac{v^2}{c^2}})}$

$\tau=\tau_0\times2.5\times10^{\frac{7}{8}}$

$\tau_0\times2.5\times10^{\frac{7}{8}}=\frac{\tau_0}{\sqrt{(1-\frac{v^2}{c^2}})}$

Both sides take square

$6.25\times10^{\frac{7}{4}}=\frac{1}{{1-\frac{v^2}{c^2}}}$

${{1-\frac{v^2}{c^2}}}=.16\times10^{\frac{-7}{4}}$

${{1-\frac{v^2}{c^2}}}=2.845\times10^{-3}$

$\frac{v^2}{c^2}=0.9971$

$\frac{v}{c}=0.9985$

$v=0.9985c$