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

AI Thread Summary
To determine how fast a pion must travel to cover 9 meters before decaying, time dilation must be considered due to its average lifetime at rest of 2.60 × 10^-8 seconds. The initial calculation suggested a speed of approximately 0.8666c, but this does not account for relativistic effects. The relevant equations involve comparing the decay time in the pion's frame versus a stationary observer's frame. Understanding the reference frames is crucial, as the pion's lifetime is shorter in the stationary observer's perspective due to time dilation. Ultimately, the correct approach involves algebraic manipulation of these equations to find the required speed in terms of c.
Herjo345
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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.
 
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Herjo345 said:
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 :wink:).
 
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?
 
I figured it out, thank you for your help.
 
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