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Ionian32492
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Homework Statement
A Rocket Moves away from the Earth at a speed of (3/5)c. When a clock on the rocket says that one hour has elapsed, the rocket sends a signal back to the earth.
(A). According to clocks on the earth, when was the signal sent?
(B). According tot eh Clocks on the earth, how long after the rocket left did the signal arrive at the earth?
(C). According to an observer on the rocket, how long after the rocket left did the signal arrive at the earth?
Homework Equations
[itex] \Delta t = 3600s [/itex]
[itex] \beta = \frac{v}{c} = 0.6[/itex]
[itex] \gamma = \frac{1}{(1-\beta^2)^.5} [/itex]
[itex] \Delta t' = \Delta t \gamma [/itex]
The Attempt at a Solution
For part A:
[itex] \gamma = \frac{1}{(1-\beta^2)^.5} = 1.25 [/itex]
[itex] \Delta t' = \Delta t \gamma = 4500s [/itex]
This much I think is correct.
For part B:
[itex] \Delta t_t = \Delta t_1 + \Delta t_2 [/itex]
[itex] \Delta t_1 = \gamma \Delta t [/itex]
[itex] \Delta t_2 = \frac{d_{rocket}}{c} [/itex]
[itex]d_{rocket}=\gamma \beta c \Delta t = 2700c seconds [/itex]
[itex] \Delta t_t = \gamma \Delta t + \frac{d_{rocket}}{c} [/itex]
[itex] \Delta t_t = 4500s + 2700s = 7200s = 2hr [/itex]
I don't feel comfortable with this answer. I found an analogous question in my textbook regarding time dilation and length contraction, and it followed the same procedure I did, but I feel my answer should just be double the time the rocket observed.
I've yet to do part C, to be frank I'm so burnt out on the last two parts that I've yet to get to it. When I get to it, I will edit this.
EDIT: Part C
[itex] \Delta t_t = \Delta t_1 + \Delta t_2 [/itex]
[itex] \Delta t_1 = \Delta t = 3600s [/itex]
[itex] \Delta t_2 = \frac{\Delta x}{c} [/itex]
[itex]\Delta x=\beta c \Delta t = 2160c seconds [/itex]
[itex] \Delta t_t = \Delta t + \frac{\Delta x}{c} [/itex]
[itex] \Delta t_t = 3600s + 2160s = 5760s = 1hr 36 min [/itex]
Followed the same procedure, but from the reference point of the rocket. Comparing to part b, it seems to coincide with the results of the Twin Paradox, so I feel good about this one.
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