Velocity of relativistic spaceship

[Rct33]

Homework Statement

A spaceship travels from Earth to a star that is 6 light years away. The spaceship takes 2.5 years to reach the star in its frame. Calculate the velocity of the spaceship.

Homework Equations

$x=\frac{x_0}{γ}$, $t=γt_0$

The Attempt at a Solution

I guess I have to relate the two equations to work out velocity somehow. Previous attempts where I considered the distance, $6ly$ divided by the velocity of the spaceship was equal to the time it takes to travel to the star as seen on Earth. I then substituted $t$ for $γt_0$ where $t_0=2.5y$ and rearranged to find $v$, but this was unsuccessful. I don't have any other ideas to try so hints would be appreciated.

 

[mfb]

Your approach looks good. Please show your work so we can see where the calculations went wrong.

 

[Rct33]

$\frac{6}{v}=t=2.5γ$ where the velocity is a fraction of c, 6 is in light years and t, 2.5 are in years.

Implies:

$\frac{6}{2.5}=\frac{v}{\sqrt{1-\frac{v^2}{c^2}}}$

$∴v=\frac{12c}{\sqrt{25c^2 + 144}}=2.4$ solved with wolfram because tired

Can't understand why I get 2.4c as an answer?

 

[Chestermiller]

$\frac{6}{v}=t=2.5γ$ where the velocity is a fraction of c, 6 is in light years and t, 2.5 are in years.

That should be: $\frac{6c}{v}=t=2.5γ$

Chet

 

[Rct33]

That should be: $\frac{6c}{v}=t=2.5γ$

Chet

Cheers

 

[mfb]

$$\frac{6}{2.5}=\frac{v}{\sqrt{1-\frac{v^2}{c^2}}}$$
This has a solution with v smaller than 1.

$$∴v=\frac{12c}{\sqrt{25c^2 + 144}}=2.4$$ Don't use c here (or plug in 1), as you worked with years=speed of light = 1 anyway.

A proper calculation with units would not have this issue...