Relativity: Spaceship travel times and distances

[annalian]

Homework Statement

A star is 95.0 year lights away from Earth. How much time does it take to a cosmic ship, which moves with speed 0.96 c, to reach the star, if it is measured from a watcher from a) Earth a)ship c)What si the distance of trip, based on the viewer from the ship?

Homework Equations

t=L/v
Lr=L*sqrt(1-v^2/c^2)

The Attempt at a Solution

a) t=L/v=99 years
c) Lr=L*sqrt(1-v^2/c^2)=26.6 years
b) tr=Lr/v=27.7 years.
I'm not sure if for this I should use tr=t/sqrt(1-v^2/c^2). Which one is the best to use because the results are different. But if I use tr=t*sqrt(1-v^2/c^2) it has the exact same result. If 27.7 years is the correct answer, then why should the length contract and time not dilate?

 

[BvU]

Is your problem description complete ?
In part a) , what do you use for L and what do you use for v to get 99 y ?

 

[annalian]

Is your problem description complete ?
In part a) , what do you use for L and what do you use for v to get 99 y ?

I had forgotten to put the speed. it is 0.96 c