Question

a certain particle has lifetime of 2.2us when measured at rest. how fat does it goes on average before decaying if its speed is 0.99cwhen it's created

Answer 1

As we know when a particle move with a velocity close to that of light then the clock in moving frame is delayed as measured from lab frame. Hence due to speed of the particle, particle's life time(T) in lab frame will be higher by a factor of $\gamma =\cfrac{1}{\sqrt{1-\cfrac{v^2}{c^2}}}$ . Where 'v' is the speed of the particle. Hence

$$T=\gamma\tau$$ $$2.2\times10^{-6}\times\cfrac{1}{\sqrt{1-0.99^2}}\\ T=15.59\times10^{-6 }sec$$

Now distance(d) travelled by particle before decay...

$$d=v\times T=0.99\times3\times10^8\times15.59\times10^{-6}\\ d=46.30\times10^2 meter.....Ans$$