Find the velocity using special relativity

[Qazzy03]

[SOLVED] Find the velocity using special relativity

According to observations on the Earth, the nearest star to the solar system is 4.25 light years away.
A spaceship which leaves the Earth and travels at uniform velocity takes 4.25 years, according to the ship-borne clocks, to reach the star.
What is the speed of the space ship, expressed as a fraction of the speed of light c?



Ux = (U'x + v)/(1 + v*U'x/c^2)
We know that: x = 4.25 light years
t' = 4.25 years
c = constant.




I have been stuck on this question for nearly a week, and i was hoping someone could give me a push in the right direction. Now i know about time dilation and length contraction and that they will be seen differently between the two frames. Thats why i don't suggest that the v of the ship is equal to c.
I have also tried to rearrange the equation using Lorentz transformations, however in most cases i need gamma which means i need v.
Any suggestions would be a great help, Thanks.

 

[Dick]

Pick one frame to work from. The simplest is earth. The time in this frame that the ship takes is 4.5*v/c years, yes? Now put the the gamma factor (leaving v as unknown) to get the elapsed ship time. Set it equal to 4.5 years and solve for v.

 

[Qazzy03]

Thank you for the help, i now see how it works and i am able to solve v.