Help with a hard special relativity question?

I understand the basic concepts of special relativity, but I can't figure out how to solve this question, remembering that both length and time change.





The star Alpha Centauri is 4 light years away. At what constant velocity must a spacecraft travel from Earth if it is to reach the star in 3 years, as measured by the travellers on the spacecraft?


Thanks.|||It takes the ship 3 years to reach the star while


moving at v. Hence the contracted distance is:


D = v*t = v*3 = 4c*sqrt(1-v^2/c^2)


=%26gt;v = sqrt(16/25)c|||Thank you.

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|||1 Lightyear = 9.461 * 10^15 meters





Velocity = Distance/Time





Velocity = 4(9.461 * 10^15m) / (3(60s)(60)(24)(365)) (This value here is the equivalent of 3 years in seconds (3, 60 seconds, 60 minutes, 24 hours, 365 days))





Velocity = 400008455.9m/s