Not enough information for question? [1st year special relativity]

[radiator0505]

Homework Statement

I've been going over past papers recently and I can't see how to start this one, I get confused with the reference frames and it looks like I don't have enough information to start this.

"An unspecified meson has a mean lifetime , defined in its rest frame, of t = 2.60x10^-8. The meson decays into a muon and a neutrino. At what speed does the meson have to be moving for it to travel a distance of 20m in the lab frame?"

Homework Equations

T=γt
L=l/λ
v=s/t (not sure about this one, would i need to use the relativistic velocity?)

The Attempt at a Solution

I can't see how to start, if I could figure out gamma or either of τ and l I think I can do it.

 

[Doc Al]

Hint: γ is a function of v, so an equation with γ can be written in terms of v.

Pick either frame to work with. One frame you'll need length contraction; the other frame you'll need time dilation. Take your pick!

 

[radiator0505]

But how do I find (for example) t?
I can;t just use v=s/t can I?

 

[Doc Al]

But how do I find (for example) t?

The time is given (at least in the muon's frame). It must travel the given distance before it decays.

I can;t just use v=s/t can I?

Sure you can.

 

[radiator0505]

Sure you can.

Really? Does it not matter that the particles relativistic?
Is the only frame where stuff like v=s/t doesn't hold a relativistic one?

 

[loba333]

I think what DocAl is getting at is in the observers reference frame you can use v=s/t as your just trying to find out how long it takes for the meson to travel that distance. This is how long it will take as seen by the observer, however the clock on the meson is ticking much slower and relativity should be used when working in the mesons reference frame

 

[Doc Al]

Really? Does it not matter that the particles relativistic?
Is the only frame where stuff like v=s/t doesn't hold a relativistic one?

v = s/t works in any frame and for any speed. It's the definition of speed.

Just be sure that you use the distance and time measurements from the same frame. Don't mix distance from one frame with time from another.

Relativity comes into the picture when you want to transform distance or time measured in one frame to that measured in another. And that's exactly what you need to do here, since the time and distance that you are given are from different frames. Pick one and go for it.

 

[loba333]

well i was wrong. thanks DocAl. Do you know anything about QM? do u think you could help me out wit my most recent post ?

 

[radiator0505]

v = s/t works in any frame and for any speed. It's the definition of speed.

Just be sure that you use the distance and time measurements from the same frame. Don't mix distance from one frame with time from another.

Relativity comes into the picture when you want to transform distance or time measured in one frame to that measured in another. And that's exactly what you need to do here, since the time and distance that you are given are from different frames. Pick one and go for it.

Brilliant, completely cleared that up.
Thanks!