I am not going to use the numbers you gave me because it is
my preference to do a problem in general; you can stick the numbers in. The speed of the space ship as seen by the
space station I will take as ,
the speed of the laser in both frames is *c*, the speed of the rocket in
the space ship frame I will take as (Note that I assume that the space ship is
moving *toward* the space station; if it were moving away you would have
to replace *β *by*
**−β* everywhere.)
The speed of the rocket in the space station frame is obtained from the
velocity addition formula:

.

In the space station frame, the distance which must be
traveled I will take to be *L* (the distance to the ship when it
fires. So it is now straightforward to
calculate the times *t* (the time for the laser) and *t _{R}*

and

.

Next we find the times and as seen by the space ship. Two things have to be taken into consideration: the distance between the two is length-contracted, , and in the time (or ) the space station moves up a distance (or ) to “meet” the laser (or rocket). So, now,

;

and

.