Originally Posted by ahbee Our galaxy is about 10^5 light years in diameter.
(a) How fast would a spaceship have to travel in order to cross the galaxy in 300 years as measured from within the spaceship? 
$\displaystyle t' = \gamma t = \frac{t}{\sqrt{1  \frac{v^2}{c^2}}}$
where t' = 300 years. Notice that the ship is going at a speed v in the stationary frame so we also know that
$\displaystyle t = \frac{x}{v}$
where x is the length of the Galaxy.
Thus
$\displaystyle t' = \frac{\frac{x}{v}}{\sqrt{1  \frac{v^2}{c^2}}}$
$\displaystyle t' = \frac{x}{v \sqrt{1  \frac{v^2}{c^2}}}$
(b) How much time would elapse on Earth during the transversal?

As I mentioned above
$\displaystyle t = \frac{x}{v}$
Dan