How Fast is the Rocket Traveling According to Earth's Time Reference?

[PsychonautQQ]

Homework Statement

A star is 27c*y away from the rest reference of earth. A rocket reaches star A from Earth and according to clocks on it 12 hours have passed. How fast is the rocket traveling in Earth's reference frame?

Homework Equations

tpγ=t
Lp/γ=L

The Attempt at a Solution

The problem is under the category of length contraction and time dilation so I assume these are the two equations I must use. However when trying to do the problem I only was given t and Lp, and yet there are three variables (tp, L, and v). Help ;-(

 

[Enigman]

Can you calculate what time has passed wrt IR_earth?
(I am assuming Earth is assumed to be an IR and the ship doesn't accelerate.)

 

[PsychonautQQ]

yes, no acceleration.
I don't think I can calculate the time wrt IRearth..? I would need to know the velocity to do that so I knew the gamma factor correct?

 

[Enigman]

v_earth=d_earth/t_earth
t_earth=d_earth/v_earth
plug and chug.

 

[PsychonautQQ]

I don't know t_earth though? I only know it took 12 years from the spaceships frame..? oh... is Vearth 27c*y / 12 years...? I'm a noob X_X

 

[PsychonautQQ]

but that's not REALLY the speed Earth see's it moving is it? Because Earth couldn't see the rocket traveling faster than C could it?

 

[Enigman]

v_earth=d_earth/t_earth
t_earth=d_earth/v_earth
plug and chug.

t_earthγ=t
or, t_earth=t/γ
equate the t_earth
Quadratic eq in v^2*_earth
*editted