In its own frame of reference, a proton takes 5 minutes tocross the Milky Way ga

Question

In its own frame of reference, a proton takes 5 minutes tocross the Milky Way galaxy, which is about 10^5 light years indiameter. a) What is the approximate energy of the proton in eV? b) About how long would the proton take to cross the galaxy,as measured by an observer in the galaxy's reference frame? In its own frame of reference, a proton takes 5 minutes tocross the Milky Way galaxy, which is about 10^5 light years indiameter. a) What is the approximate energy of the proton in eV? b) About how long would the proton take to cross the galaxy,as measured by an observer in the galaxy's reference frame?

Explanation / Answer

a)the approximate energy of the proton K = (1/2)m * v^2 m = 1.67 * 10^-27 kg v = (d/t) d = 10^5 light years = 10^5 * 9.46 * 10^15 m = 9.46 * 10^20m t = 5 minutes = 5 * 60 s = 300 s or v = (9.46 * 10^20/300) = 3.15 * 10^18 m/s b)the time taken by the proton is t = (to/(1 - v^2/c^2)^(1/2)) to= 300 s v = 3.15 * 10^18 m/s and c = 3 * 10^8 m/s

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