(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

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?

2. Relevant equations

t=[tex]\gamma[/tex]t_{0}

d=[tex]\gamma[/tex]d_{0}

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

v=d/t

3. 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 t_{0}to t, so I had

(using t(naught) as t_{0}, 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 t_{0}= 10yr and d= 130 pc

I got that v=2.9996*10^{8}m/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, but I don't quite understand latex, so there may be somethings that look ugly and I also posted this in advanced physics by accident, so I posted it again here, as its not that advanced, if someone could delete or move the otherone or something, sorry for confusion.

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# Velocity in Special Relativity

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