# Homework Help: What would happen if you travelled at 3/5 c

1. Sep 28, 2004

### stunner5000pt

using Relativistic mechanics
Gamma = 1 / (Root (1/ v^2/c^2))
The target area in a lab in a straight line tube of 400 m long. 1 million radioactive particles are shot in this tube at (3/5) c . Half of them will arrive at the other end without decaying. To the observer moving with the particle:

a) how long is the tube measured to be?
shorter than 400m, i would think it's 400 / gamma = 400 / 1.25 = 320m

b) what is the half life of the particles?
is this as easy i think it is? t = D/ v = 400 / (3/5)c = 2.22 x 10^-6 s and thus half life is 1.11 x 10^-6 s

c) What is the speed the tube is measured to move?
in the opposite direction at (3/5)c?

2. Sep 28, 2004

### Staff: Mentor

Right.

Half-life should be measured in the rest frame of the particles. (You measured the travel time according to the lab frame.)

Right.

3. Sep 28, 2004

### stunner5000pt

For the B Part is the following correct??

since the distnace travelled in the lab fram is 400 m, and velocity is 3/5c then the time is 2.22 e -6 s

furthermore, the half life is given by 2.22e-6 / gamma = 1.776 e -6s