Lorentz Transformation/converting between reference frames

[bmb2009]

Homework Statement

Particle track detectors are used to measure the speed of particles if the lifetime of the particle is known. Particle X has a lifetime of 256.2 ps. These particles are created in an experiment inside the detector by a given reaction. The particles leave 21.8 cm long tracks on average before they decay into other particles not observable by the detector.
What is the average speed of the particles in terms of the speed of light?

Homework Equations

Lorentz Transformation equations..

The Attempt at a Solution

The particle's life time is given in the moving reference frame and the track distance is given in the reference frame...so I need to convert either value to the other frame and then the velocity is just the distance traveled divided by the lifetime but how do I transform from either reference frame with the given information? It seems like there is not enough information. Help?

 

[diazona]

Have you tried it though?

Remember that you can use a variable for the velocity.

 

[bmb2009]

I tried to get as far as I could and I did use a variable for the velocity, the part that I didn't understand how to manage was the transformations.. i.e if L=lorentz factor:
x=L(x'+vt') ..here I kept v as a variable but how would I solve for x when only give t' and not x' as well?

 

[diazona]

Ah, you've been trying to do it the hard way. Do you know the formulas for time dilation and length contraction?

 

[bmb2009]

actually just went over those today in class which made the problem way easier than i originally thought. Thanks for the guidance!