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.