How Long Will It Take to Travel 65 Light-Years at Relativistic Speeds?

[persephoneia]

Homework Statement

Suppose you decide to travel to a star 65 light-years away at a speed that tells you the distance is only 25 light-years. How many years would it take you to make the trip?

Homework Equations

∆t=∆t₀/(√ (1−v²/c² )) / ∆t₀ = ∆t √(1−v²/c²)
L=L₀√ (1−v²/c²)

The Attempt at a Solution

I've attempted to use the length contraction equation to find the velocity (v=c√(1-(25/65)^{^2}) but when I plug that into the time dilation equation I don't get the correct answer. I get 25 when the answer should be 27. Where am I going wrong?

 

[PeroK]

Homework Statement

Suppose you decide to travel to a star 65 light-years away at a speed that tells you the distance is only 25 light-years. How many years would it take you to make the trip?

Homework Equations

∆t=∆t₀/(√ (1−v²/c² )) / ∆t₀ = ∆t √(1−v²/c²)
L=L₀√ (1−v²/c²)

The Attempt at a Solution

I've attempted to use the length contraction equation to find the velocity (v=c√(1-(25/65)^{^2}) but when I plug that into the time dilation equation I don't get the correct answer. I get 25 when the answer should be 27. Where am I going wrong?

If you know the distance in your frame and the velocity in your frame, what do you need time dilation for?

 

[persephoneia]

If you know the distance in your frame and the velocity in your frame, what do you need time dilation for?

I don't. I wasn't thinking that light years is also a distance because I looking at an example for the problem that combined the two equations (length contraction & time dilation) which threw me off. It's basically t=d/v after you figure out velocity right?

 

[PeroK]

I don't. I wasn't thinking that light years is also a distance because I looking at an example for the problem that combined the two equations (length contraction & time dilation) which threw me off. It's basically t=d/v after you figure out velocity right?

Right!