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Time Dialation Help

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[SOLVED] Time Dialation Help

1. Homework Statement
A bomb is placed on a space probe just before it's launched. The timer is set to trigger the bomb after exactly 24hrs. The probe travels away from Earth on a straight line at v=.9c. How long after launch will the observers on the Earth see the flash of light from the exploding bomb?


2. Homework Equations

[tex]\Delta\tau=\Delta t \sqrt{1-\frac{v^{2}}{c^{2}}}[/tex]

3. The Attempt at a Solution
[tex] \Delta\tau = 24hrs.[/tex]

[tex]\Delta t = \frac{24hrs}{\sqrt{1-.9^{2}}} = 55hrs[/tex]
But, the text book gives a time of 105hrs. Can anyone please tell me why what I did is wrong? This seems like a straightforward problem and I have no clue where I mesed up. Any help is greatly appreciated.
 

Answers and Replies

196
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You're half way,
I think you need to add time for the light from the explosion to get back to earth - which is when people on earth see the explosion
Calc how far away it is.
Then calc the time for light to travel that distance.
 
208
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Then,
[tex]\Delta x = .9c(55hrs)[/tex]
[tex]t = \frac{.9c(55hrs)}{c} = 49.5 hrs [/tex]
[tex]55+49.5=104.5[/tex]

Thank you for the help, I completely blanked that part!
 

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