How Far Can a Particle Travel at 0.99c Before Decaying?

[asdf1]

can someone help with this question?


A certain particle has a lifetime of 1*10^(-7) sec when measured at rest. How far does it go before decaying if its speed is 0.99c when it is created?

 

[H_man]

Well... I'd start this problem by putting it into the Lorentz formula and seeing the amount of time it would take for it to decay as observed by a stationary observer.

I'd then multiply this time with the speed at which it is travelling.

 

[asdf1]

@@a
why'd you use the lorentz formula?

 

[El Hombre Invisible]

He means the time dilation application of the Lorentz transformation. The particle still decays at the same rate in its own reference frame, but in an observer's frame in which it is traveling at 0.99c, this time interval is dilated: T' = T/root(1 - (v/c)^2).