(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

In its own frame of reference, a proton takes 5 min to cross the Milky Way galaxy, which is about [tex]10^{5}[/tex] light-years in diameter.

(a) What is the approximate energy of the proton in electronvolts?

(b) About how long would the proton take to cross the galaxy as measured by and observer in the galaxy's reference frame?

2. Relevant equations

[tex]T = \frac{T_{0}}{\sqrt{1-\frac{v^{2}}{c^{2}}}}[/tex]

[tex]L = L_{0} \sqrt{1-\frac{v^{2}}{c^{2}}}[/tex]

mass of proton = [tex]1.6726x10^{-27} kg[/tex]

3. The attempt at a solution

I assume the first thing I need to find is the velocity of the proton. Is that right?

first I calculate the distance in meters:

so [tex]10^{5}[/tex] light-years = [tex]9.45x10^{20} m[/tex]

Then I set up the equation with time in seconds (5min = 300s) (going to leave out units):

and [tex]T_{0}[/tex] is found by (distance/velocity) so (the distance above in meters)/v

[tex]300 = \frac{9.45x10^{20}}{v \sqrt{1-\frac{v^{2}}{c^{2}}}}[/tex]

Anyways, when I run into problems when I try and solve this.

Also the book shows the answer, which I have copied below exactly how it appears in book:

~[tex]10^{19} eV;[/tex] ~[tex]10^{5} y[/tex]

So I'm assuming they used some kind of approximations, because If I use those values and work backwards I get a velocity of 1c I'm assuming the real velocity is like .99999c ect.. But my calculator just rounds off after so many digits.

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# Homework Help: Special relativity. energy

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