A spaceship travels from Earth to the vicinity of the star that is measured
by astronomers on Earth to be six light-years away. The spaceship
and its occupants have a total rest mass of 32 000 kg. Assume that the
spaceship travels at constant velocity. The time taken as measured by
clocks on the spaceship is 2.5 years
i) Calculate the velocity of the spaceship.
There are other parts but I think once I find the velocity I should be able to do them
I'm not sure exactly if it's using Lorentz transformations or just time dilation/length contraction. In any case here are those formulae:
L=L 0 /γ
Δx ′ =γ(Δx−vΔt)
Δt ′ =γ(Δt−vΔx/c 2 )
The Attempt at a Solution
So I set the distance from Earth to the star as the standard length, L 0, and the time taken as measured by the spaceship to be ΔT. To find the velocity I then tried to find either ΔT 0 or L to substitute into v =Δx/Δt but to compute both I needed the velocity for γ.
Of course I tried it algebraically, solving for v but ended up with a polynomial I couldn't solve. I can post the working if necessary but I have a feeling I've made a more fundamental error with my reference frames which are still confusing me a bit.
Please help me physicsforums, you're my only hope!