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**[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 space ship 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?

A space ship 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.

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.

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.