Proton passes the Milky Way galaxy, find its energy?

[asdf1]

for the following question:
In its own frame of reference, a proton takes 5min to cross the Milky Way galaxy, which is about 10^5 light-years in diameter.
What is the approximate energy of the proton in electronvolts?

my problem:
v*5*60=(10^5)*3*(10^8)*[1-(v^2/c^2)]
however, i can't calulate v on the calculator, because v is too small...
i was trying to use E=(1/2)mv^2, where m is the photon rest mass...
is that right?

@@a

 

[quantumdude]

v*5*60=(10^5)*3*(10^8)*[1-(v^2/c^2)]

This looks like algebraic soup! Why, oh why, are you combining these quantities together in this way? From what equation are you working?

It looks like:

$$vt=\frac{Dc}{\gamma ^2}$$

where $v$ is the proton speed in the galaxy frame, $D$ is the galactic radius in the galaxy frame, and $t$ is the travel time in the proton frame.

however, i can't calulate v on the calculator, because v is too small...
i was trying to use E=(1/2)mv^2, where m is the photon rest mass...
is that right?

No, it's not right. The photon rest mass is zero.