[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.