Does Flying Across Australia Affect Your Age?

AI Thread Summary
Flying across Australia at 250 m/s results in aging less than friends at home due to time dilation effects described by relativity. The traveler’s total time, including the return trip, is calculated to be 192 hours. The formula for time dilation, Δτ = Δt - 0.5β²Δt, is applied to find the difference in aging. The user struggles with calculating the correct time value and seeks clarification on achieving a result in the order of 10^-8 seconds. Assistance is requested to resolve the confusion in the calculations.
fredrick08
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Homework Statement


You fly 5000 km across Australia on an airliner at 250 m/s. You return two days later.
(a) Have you aged more or less than your friends at home?
(b) By how much?
Hint: Use binominal approximation.


Homework Equations


\Delta\tau=\sqrt{}1-\beta^2*\Deltat
t=x/v


The Attempt at a Solution


ok a. is aged less.
b. I am a bit stuck on.. I am doing it like this..
t=(x/v)+48hrs=10000/(250/3.6)+48=192hrs.
then \Delta\tau\approx\Deltat-.5\beta^2*\Deltat=192-.5((250/3x10^8)/3.6)^2*192=192hrs?
im pretty sure this is wrong, probably doing it all wrong could someone please help?
 
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ok i know the answer has to be like something 10^-8 s or something... but i just don't see how to it?? I am sure its my t value... but don't know why, please someone help
 
anyone at all?
 

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