Calculating Distance and Time for Traveling to a Star at 1.0x10^8 m/s

[msimard8]

A star is measured to be 40.0 ly from Earth, in the inertial frame in which both star and Earth are at rest.

A) what would you determine this distance to be if you travveled to the star in a spaceship moving at 1.0x10^8 m/s relative to earth.

answer is 37.7 ly (calculated that, with no problem)

b) How long would you determne the journey to take?

ok this is where i get stumpped

I converted ly to m and got some result.
do u convert this distance to time using v=d/t

if you do that what do you after?

where do i go from here?
thanks

 

[malawi_glenn]

According to Earth's frame where the star is at rest, it would take the time 120 years since 1.0x10^8 m/s is c/3
The event in Earth's frame is the coordinate (x,ct) = (40, 120) light-years
Use the Lorentz-transformation to obtain the coordinates of that event in the starships rest frame

 

[Steve4Physics]

In addition to what @drmalawi has said, and given the age (15+ years) of the question, can I add some hints for future readers...

37.7 ly for part a) is correct (easily determined using the Lorentz length-contraction formula). This value can then be used to answer part b) directly.

The Earth and star are at rest in some inertial frame. It follows that for an observer on the rocket, the star is seen to approach at speed ⅓c.

The duration of the journey as measured on the rocket’s frame is simply distance/speed, using the values from the rocket's frame. The distance to be covered in the rocket’s frame is 37.7 ly (from part a).

There’ s no need to convert to SI units; work in units with distance in ly, time in years, and c = 1 (ly/y).

v = 1.0x10⁸ m/s = ⅓c (accurate enough for this problem)

t = distance/speed = $\frac {37.7}{⅓}$ years