- #1

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]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

## 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, sorry but I don't quite understand latex, so there may be somethings that look ugly.

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