Pion in rest frame and lab frame

[monke]

Homework Statement

An unstable particle called the pion has a mean lifetime of 25ns in its own rest frame. A beam of of pions travels through the lab with a speed of 0.60c.
a) what is the mean lifetime of the pions as measured in the lab frame?
b) how far does a pion travel ( as measured by lab observers) during this time?

Homework Equations

I was able to find part a but not sure about part b. the answer our professor porvided was 5.6m
what exactly is c? is it unit less?

The Attempt at a Solution

I found a using

t= 1/γ x t inital

for finding how far the pion traveled i was using

d=v t with 0.60 for v and 31ns for t.

however the units are not correct and my answer is not very clse to the given answer.



Thanks in advance :)

this gave me an answer of 31 ns.

 

[BruceW]

for finding how far the pion traveled i was using

d=v t with 0.60 for v and 31ns for t.

I'm guessing you meant to type 25ns here?

I found a using

t= 1/γ x t inital

I'm not sure what you mean by t initial. If it means time according to the rest frame, then the equation is wrong, because it should multiply with gamma, not one over gamma. But you do have the right answer of 31ns.

for finding how far the pion traveled i was using

d=v t with 0.60 for v and 31ns for t.

however the units are not correct and my answer is not very clse to the given answer.

the question tells you that the pions are traveling at 0.6c, and since you have used SI units in the rest of the equation, c is not just equal to 1. (In relativity questions, c is very often used to mean the speed of light, in case you had any doubts about what it was meant to represent).

 

[monke]

thank you :)

 

[monke]

one more question when working problems like this and others with realtive velocity c will always be the speed of light value ? if so then how can something such as V=0.50c be able to be sub in for v^2/c^2

 

[BruceW]

the symbol c is almost always used to mean the speed of light in vacuum (unless they specify otherwise), which is always 3*10^8 m/s (or roughly that, anyway). When you have v=0.5c and want to find v^2/c^2, just sub it in:
$$\frac{(0.5c)^2}{c^2}$$
And you can simplify this