Solve Time Dilation: Get 24hr Solution in 105hrs

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SUMMARY

The discussion addresses a physics problem involving time dilation and the observation of an explosion from a space probe traveling at 0.9c. The initial calculation of time dilation resulted in 55 hours, but the correct total time observed on Earth is 105 hours. This discrepancy arises from neglecting the time it takes for light to travel back to Earth after the explosion, which adds approximately 49.5 hours to the observed time. The final calculation confirms that the total time is indeed 104.5 hours, aligning closely with the textbook's answer.

PREREQUISITES
  • Understanding of special relativity concepts, particularly time dilation.
  • Familiarity with the equation for time dilation: Δτ = Δt √(1 - v²/c²).
  • Basic knowledge of the speed of light and its implications in physics.
  • Ability to perform calculations involving relativistic speeds and distances.
NEXT STEPS
  • Study the implications of time dilation in special relativity using "Einstein's Theory of Relativity".
  • Learn how to calculate light travel time for various distances in "Fundamentals of Astronomy".
  • Explore more complex scenarios involving relativistic speeds in "Introduction to Modern Physics".
  • Practice solving similar problems using "University Physics with Modern Physics" by Young and Freedman.
USEFUL FOR

Students of physics, educators teaching special relativity, and anyone interested in understanding the effects of high-speed travel on time perception.

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[SOLVED] Time Dialation Help

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?


Homework Equations



\Delta\tau=\Delta t \sqrt{1-\frac{v^{2}}{c^{2}}}

The Attempt at a Solution


\Delta\tau = 24hrs.

\Delta t = \frac{24hrs}{\sqrt{1-.9^{2}}} = 55hrs
But, the textbook 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.
 
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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.
 
Then,
\Delta x = .9c(55hrs)
t = \frac{.9c(55hrs)}{c} = 49.5 hrs
55+49.5=104.5

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

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