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Owen-
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Homework Statement
A spaceship travel from Earth [itex]\alpha[/itex]-Centauri (4.3 light years away) at a constant velocity. If the time elapsed onboard during the journey is 4.e years, what is the speed of the spaceship?
The spaceship is powered by a drive which works by ejecting protons behind the ship at a velocity relative to the ship of c/2. At what velocity would a person on Earth observer the protons to be travelling, just as the spaceship reached constant velocity as it passed Earth on its way to [itex]\alpha[/itex]-Centauri
Homework Equations
[itex]\gamma=(1-\beta^2)^{-1/2}[/itex]
[itex]\beta = \frac{v}{c}[/itex]
[itex]x'=\gamma(x-vt)[/itex]
[itex]t'=\gamma(t-\frac{x \times v^2}{c^2})[/itex]
The Attempt at a Solution
[itex]x'=\gamma(4.3-vt)[/itex]
[itex]4.3=\gamma(t-\frac{x \times v^2}{c^2})[/itex]
Well essentially I couldn't see any way to cancel things with simultaneous equations, and without one other variable known I assumed it to be impossible, unless they want the answer to be in terms of something. Is this correct? Any help, even a hint in the right direction would be much appreciated. :)
Thanks in advance,
Owen.
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