# Math Help - Relativety Question

1. ## Relativety Question

if a particle is moving with a speed v with respect to Earth, for what value of v/c will the lifetime of the particle be increasesd by 10% above its lifetime when at rest?

(i know its not entirely a math question... bu i cant figure out the math involved)

2. If the lifetime of the particle at rest is t, its lifetime when moving at speed v will be $\frac{t}{\sqrt{1-\frac{v^2}{c^2}}}$.

So you need to solve the equation

$\color{white}.\quad.$ $\frac{t}{\sqrt{1-\frac{v^2}{c^2}}}\ =\ \left(1+\frac{1}{10}\right)t$

That should give $\frac{v}{c}=\frac{\sqrt{21}}{11}\approx41.66\%$.