[Special Relativity] - Time Dilation

[ajclarke]

Homework Statement

If a cosmic ray proton has 15J of energy how long, according to the proton's proper time would it take to travel from the galaxy M31 to our Galaxy, a distance that we mesure as 2.5x10⁶ light-years?

Homework Equations

K.E = m_{o}c^2 (\gamma -1)

The Attempt at a Solution

I work out \gamma to be 9.962 \times 10^{10} and then using the usual equation for \gamma I get the velocity to be c.

In our frame T=\frac{\Delta X}{c} = 7.89 \times 10^{13} seconds

Proper time \tau=\frac{T}{\gamma}=\frac{7.89 \times 10^{13}}{9.962 \times 10^{10}} = 792.01 seconds.THis isn't for an assessment, I am revising for me end of year exam looking through past papers. Anyone give me some indication if this is correct and if not, where my mistakes are.

THanks a bunch.
Adam

 

[gomboc]

I can't see anything wrong with it, assuming you solved for \gamma correctly. It looks about right though.