How Fast Must a Pion Travel to Cover 9 Meters Before Decaying?

[Herjo345]

How fast must a pion be moving, on average, to travel 9.0 m before it decays? The average lifetime, at rest, is 2.60 ✕ 10-8 s. (Answer in terms of c)

I'm not exactly sure what equations I have to use but I believe it relates to time dilation.


I originally didn't realize it was a time dilation problem and calculated that the speed would be .8666c but since it relates to time dilation I am not sure how to go about solving it.

Thank you for your help.

 

[collinsmark]

How fast must a pion be moving, on average, to travel 9.0 m before it decays? The average lifetime, at rest, is 2.60 ✕ 10-8 s. (Answer in terms of c)

I'm not exactly sure what equations I have to use but I believe it relates to time dilation.I originally didn't realize it was a time dilation problem and calculated that the speed would be .8666c but since it relates to time dilation I am not sure how to go about solving it.

Thank you for your help.

You have a bit of algebra ahead of you. But let's just set up the equations first.

If $\tau$ is the time it takes the pion to decay in it's own frame of reference ($\tau$ = 2.60 × 10^-8 s), what is t, the amount of time it takes to decay in your stationary frame of reference?

(you can answer this intermediate result in terms of c and v; or in terms of $\gamma$, your pick for now ).

 

[Herjo345]

I could use the equation (ΔT/Δt)=√(1-(v/c)^2) but I'm still a little unsure on the reference frames. Is the first reference from from the pion and the second from a stationary observer?

 

[Herjo345]

I figured it out, thank you for your help.