Thank you DrDusk and blyatman for your responses. It is much appreciated.
How would I go about doing this question then.
A star is 27 light-years away according to earth observers. (Note: A light-year is the distance travelled by light inan earth year.) How long would it take a spaceship travelling at 0.90c to reach the star from earth as measured by observers (a) on earth; (b) on the spaceship?
Thanks
This is not a question of time dilation, but rather of Length contraction.
Picture yourself standing on the Earth and imagine the distance between the Earth and The Sun as a ruler. When you measure it on the Earth you are stationary relative to this ruler, so the distance you measure is L_0 which is 27 light years. Now imagine your on the spaceship, you are then moving with respect to the ruler, so according to you on the spaceship, the ruler must contract in length giving a length L_v.
The people on the spaceship therefore have to travel a distance given by
Then by using the fact that time = distance/speed you can figure out the time it should take someone on a spaceship as measured by someone on The Spaceship, however for someone on the Earth, remember they are stationary with respect to this 'imaginary' ruler and hence they measure proper distance which in this case is 27 light years.
In general if your confused as to if a question requires time dilation or length contraction remember that time dilation comes into play with you are moving with respect to an event and want to find out the new time. In this case the event itself is the journey, how can you move with respect to the journey? You can however move with respect to the 'imaginary' ruler I mentioned which means it must be a length contraction question.