Special Relativity: Object Motion and Time Dilation

[Lucille]

Homework Statement

An object moves at v=0.94c in the frame of a laboratory for 32 us, decaying as it reached the other end.
a) how far did it move in the frame of the laboratory?
b) how long did the object travel in its rest frame?
c) in the rest frame, how long is the laboratory?

Homework Equations

t' = gamma * (-v/c^2*x + t)
x' = gamma* (x-vt)

The Attempt at a Solution

for a, I did:

x=v*t = (0.94c)(32us) =90,177.6 m

b)

t' = gamma * (-v/c^2 * x + t) = 10.9us

c)

x' = gamma * (x - vt) = 0 m

thanks!

 

[Simon Bridge]

Welcome to PF;
Good up to (c) well done.
Recall - inside each inertial frame the regular laws of physics work like normal.
In the rest frame of the particle the laboratory of length d' zips past at speed v, and it does that in time t' ... so how long is d'?

 

[Lucille]

would it be x' = vt' = 30,716.7 m? if so, i was wondering why x'=gamma*(x-vt) did not apply/could not work. thanks!

 

[Simon Bridge]

The beginning and end of the lab happen in the same place in the rest-frame of the particle.

 

[Lucille]

Oh, that makes sense! Thank you so much!