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Kamkazemoose
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Homework Statement
You wish to travel to Pleisdes (at a distance of 130 pc) in 10 years, according to the clock that you carry. How fast do you have to travel to accomplish this (express the velocity as v/c)?
When you reach the Pleisdes, you send a radio signal back to Earth. For someone on Earth, how long has it been between the moment you left and the moment when the radio signal was received?
Homework Equations
t=[tex]\gamma[/tex]t0
d=[tex]\gamma[/tex]d0
[tex]\gamma[/tex]=[tex]\frac{1}{1-\sqrt{1-\frac{v^2}{c^2}}}[/tex]
v=d/t
The Attempt at a Solution
I know that to calculate velocity, you have to use the time and distance in the same inertial frame, so we can't simply insert the given d and the given t, as they are in 2 frames. I tried to come up with an equation for velocityby converting t0 to t, so I had
(using t(naught) as t0, because i can't get it to work within latex, sorry)
v=[tex]\frac{d}{\gamma*t(naught)}[/tex]
and then, replacing gamma and using algebra etc, I simplified this to
v=[tex]\frac{d}{\sqrt{t(naught)^2+\frac{d^2}{c^2}}}[/tex]
where t0 = 10yr and d= 130 pc
I got that v=2.9996*108m/s or v=.9997c and [tex]\gamma[/tex] = 40.83
then, when I calculate t in the frame of the earth, i get t=408.3 years, but d = 424lightyears, so This should mean that the person is traveling faster than the speed of light, but I found v as less than the speed of light, so something went wrong.
If you could help, did I get the equation for finding velocity wrong, or was there something else, I can't figure it out, thanks. Also, sorry but I don't quite understand latex, so there may be somethings that look ugly.
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