Solve Relativity Problem: Photon & Proton Parallel Travel

[dingo_d]

Homework Statement

A photon and a proton with the speed v=0.485c, start to travel parallel to each other in the same direction. After one year, how much is proton behind the photon?

The Attempt at a Solution

The problem that I'm facing is, do I need to include Lorentz transformations into this, or just simply calculate the distance traveled by photon and proton, and subtract them?

Because that seems kinda too easy.

I would go with this:

I am looking at them from one point, and they go with their respective speeds in one direction parallel to each other. Since the photon travels at the speed of light, after one year it will travel s=c*1 yr = 1 light year =9.4*10^15 m.

But the proton that travels at roughly 0.5c, from my point of view will travel s= vt/gamma, right? That is ~ 4*10^15 m.

So the proton will be 5.4*10^15 m behind the photon.

Am I correct in this reasoning or?

I appreciate the help.

 

[tiny-tim]

hi dingo_d!

… do I need to include Lorentz transformations into this, or just simply calculate the distance traveled by photon and proton, and subtract them?

Because that seems kinda too easy.

relativity has nothing to do with it

everything is measured by the same (stationary) observer

s = vt ​

 

[dingo_d]

Oh, so that's kinda the trick question :D

Thanks :D