Question

The Whirlpool galaxy is about 30 million light-years away. If you were in a spaceship that could travel at half of the speed of light, the amount of time it would take you reach the Whirlpool galaxy is __ (Be specific, use a number.)
2) The whirlpool galaxy is about 30 million light-years away. If you went outside and looked at the Whirlpool, how long ago did the light that just arrived at your eye leave its home?

Answer 1

Answer:

51.96 years

2) 30 million of years

Explanation:

First we must know the travel time of the ship seen from the earth. The spaceship travels at half the speed of light, this means that the amount of time the spacecraft must spend to travel the same distance is double compared to the light, that is 60 years.

Now due to the speed of the ship, we must take into account relativistic effects, such as time dilation, this is given by:

$t'=\frac{t}{\sqrt{1-\frac{v^2}{c^2}}}$

Where t is the time measured in the ship, t' is the time measured in the earth, inertially moving with velocity v.

Rewriting for t:

$t=t'\sqrt{1-\frac{v^2}{c^2}}\\t=60\sqrt{1-\frac{(0.5c)^2}{c^2}}\\t=60\sqrt{1-0.5^2}\\t=51.96 years$

This is the amount of time it would take you reach the Whirlpool galaxy in the spaceship.

2) a light year is a measure of distance, which indicates the kilometers that light travels in a year. Thus, the light emitted by Whirlpool galaxy takes 30 million of years reaches our planet.