Special Relativity: time for light to traverse a rocket

[TheLil'Turkey]

Homework Statement

A 35 m long rocket is receding at 0.6c. From the point of view of a stationary observer, how long does it take for light to travel (a) from the bottom of the rocket to the top and (b) from the top to the bottom?

Homework Equations

t = d/v
L = L₀ / gamma

The Attempt at a Solution

a) L = 35 / gamma = 30.3 m
distance traveled by light = L + 0.6L + 0.6^2L + 0.6^3L + ... = 2.5L = 75.8 m
t = distance traveled by light/c = 2.5E-7 s

b) distance traveled by light = 1/(1 + 0.6)L = 18.9 m
t = distance traveled by light/c = 2.5E-7 s = 6.3E-8 s

Is this right? If not, please help me understand.

 

[Filip Larsen]

It is not correct. The equations you refer to in section 2 is relevant for your problem, but then you somehow calculate wrong value for gamma and get very confused about how fast light propagate showing you have missed a very special characteristic about speed of light that is fundamental to relativity.

So, can you write up an expression for gamma? And what is the speed of light in all reference frames?

 

[andrewkirk]

Other than the calculation of gamma, which I have not checked, that looks correct.
(a) can be done without the infinite series, by noting that the light travels distance tc while the top of the rocket travels distance 0.6tc, so the difference between the two, which is the length of the rocket L, must be 0.4tc. Hence t = L/0.4 c.

 

[TheLil'Turkey]

Filip: Oops. I typed 0.5 instead of 0.6 in my calculator for the speed of the rocket. L = 28.0, not 30.3. I think everything else is correct.
Andrew: Thanks for showing me another way to calculate t.