# Energy of proton moving fast (special relativity)

## Homework Statement

Given: in its own reference frame a proton takes 5 minutes to cross the Milky Way (10^5 meters).
(a) What is the approximate energy of the proton?
(b) About how long would the proton take to cross the galaxy as measured by an observer in the galaxy's reference frame?

## Homework Equations

All those equations for special relativity I imagine.
L = L0 Sqrt[1-(v/c)^2]
t = t0 Sqrt[1-(v/c)^2]

## The Attempt at a Solution

So I keep doing this over and over again, getting a wrong answer. The way I approach it is this: I think L is the distance as measured by the proton when crossing the galaxy, and t is the time the proton measures (5 minutes). Since v is the same in both reference frames (how fast the galaxy thinks the proton is moving and how fast the proton thinks the galaxy is moving) I can say that L/t = v. Using those equations I do it all out and find that v = c. Not very useful when I plug it into my equations for energy and find the proton has infinite energy. Where am I going wrong?

Also, I think this should be doable without the Lorentz transformations.