# Special relativity question

## Homework Statement

I have correctly figured out part a but am stuck on part b. Thanks for your help in advance.

An unstable particle called the pion has a mean lifetime of 25 ns in its own rest frame. A beam of pions travels through the laboratory at a speed of 0.587c.
(a) What is the mean lifetime of the pions as measured in the laboratory frame?
30.75 ns

(b) How far does a pion travel (as measured by laboratory observers) during this time?
m

## Homework Equations

[ Delta t x c (speed of light) ] / 2

## The Attempt at a Solution

using the answer from part a and converting to meters:

[(3.075E-8)(3E8)] / 2 = 4.6125 I've checked for errors and always come up with this number--which according to the web program is incorrect.

What am I not doing/understanding?

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Doc Al
Mentor

## Homework Equations

[ Delta t x c (speed of light) ] / 2 Where in the world did you get this formula?

Hint: How fast is it moving? How long is it moving for? How do you calculate distance traveled?

I got the formula from my professor.
As far as I can tell it is moving at 0.587c = 176100000 m/s for 25 ns.

Distance = rate x time.

So then I suppose I would do the following:

176100000 m/s x (2.5 x 10^-10) = 0.044025 meters?

Doc Al
Mentor
I got the formula from my professor.
It must be meant for some specific application--but not this one.
As far as I can tell it is moving at 0.587c = 176100000 m/s for 25 ns.
Why 25 ns? Stick to the lab frame.

Distance = rate x time.
That's all you need.

o.k. then,

176100000m/s x (3.075 x 10^-10) = 0.05415075 ~ 0.0542 and convert to meters = 5.4 m

Last edited:
Doc Al
Mentor
o.k. then,

176100000m/s x (3.075 x 10^-10) = 0.05415075 ~ 0.0542 and convert to meters = 5.4 m
Two things, the first being the most important:
- use a more accurate value for the time in part a (redo it); only round off at the end.

thank you I should have typed:

176100000m/s x (3x 10^8)x 30.75 (the answer from part a) = 5415075000

then convert from nano to meters (9 decimal spaces to the left) = 5.41 meters