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

a) What is the speed of proton that has relativistic γ factor of 10^10? Write as (1-ε)c

b) A proton with γ=10^10 is chased by a photon across a galaxy. Observer A at one end of the galaxy (xA=0) sees the proton at t1=0 and the photon at t2 = 1.33 x 10^-8 s. According to A, how far apart are the two particles at t1?

c) Another observer B is at another end of the galaxy (xB=10^21 m). The two observers are at rest relative to each other. At what times will B see the particles go past?

d) How many years does it take the proton to cross the galaxy according to A and B?

2. Relevant equations

L = Lo [itex]\sqrt{1 - v^2/c^2}[/itex]

Δt = Δto/[itex]\sqrt{1 - v^2/c^2}[/itex]

3. The attempt at a solution

a) Y = 1/[itex]\sqrt{1 - v^2/c^2}[/itex]

1 - v^2/c^2 = 1/Y^2

v^2/c^2 = 1 - 1/Y^2

v^2/c^2 = 1 - 1/(10^10)^2

v^2/c^2 = 1- 1/10^20

v/c = sqrt(1 - 1/10^20)

v/c = (1 - 5 * 10^-21)

v = (1 - 5*10^-21) c

Is this correct?

b) The photon covers the distance in t2 - t1 = 1.33 x 10^-8 s

The distance = c t^2

= 3 x 10^8 x 1.33 x 10^-8

= 3.99 m

Is this correct?

c) Can we say that the observer B will see the proton pass by at t3 = t1 + xB/v and the photon pass by at t4 = t2 + xB/c ?

If not, then what is the correct method?

d) Can we simply divide distance (which is 10^21 m) by speed and convert into years? If not, then what is the correct method?

For c and d, I am not sure if we need to use Lorenz transformation equations. The observers are at rest relative to each other. So I think we do not need.

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# Homework Help: A problem on time taken by relativistic particles

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