Answer:
B. 500 years
Explanation:
The light coming from the star and reaching us on the Earth travels with uniform motion (with constant velocity), so we can use the equation of uniform motion which relates distance covered, speed and time taken:
[tex]v=\frac{d}{t}[/tex]
where
v is the speed
d is the distance covered
t is the time taken
In this problem:
[tex]v=3.00\cdot 10^8 m/s[/tex] is the speed at which light travels
[tex]d=4.8\cdot 10^{15} km = 4.8\cdot 10^{18}m[/tex] is the distance that light has to cover from the star to the Earth
Therefore, by rearranging the equation, we can find the time:
[tex]t=\frac{d}{v}=\frac{4.8\cdot 10^{18}}{3.00\cdot 10^8}=1.6\cdot 10^{10}s[/tex]
And by converting into years, this time is
[tex]t=\frac{1.6\cdot 10^{10}}{(365)(24)(60)(60)}=507 y[/tex]
So, approximately 500 years: this means that the image we see of the star is 500 years old.
