Answer:
The spaceship will get to Alpha Centaur in time
Step-by-step explanation:
The complete question in English is
You're the commander of a spaceship. Your mission is to reach Alpha Centaur in five years. The distance from the sun to Alpha Centaur is 2.5 x 10^13 miles. The distance from Earth to Sun is approximately 9.3 x 10^7
miles. Your spaceship can travel at the speed of light. You know that light can travel a distance of 5.88 x 10^12 miles in a year. Can you get to Alpha Centaur in time?
step 1
Find the time it takes for the spaceship to travel from Earth to the Sun
The distance from the Earth to Sun is equal to
[tex]9.3*10^7\ miles[/tex]
The spaceship can travel at the speed of light
The light can travel a distance of [tex]5.88*10^{12}\ miles[/tex] in a year
so
using a proportion
[tex]\frac{5.88*10^{12}\ miles}{1\ year}=\frac{9.3*10^7\ miles}{x}\\\\x=(9.3*10^7)/5.88*10^{12}\\\\x=1.58*10^{-5} \ years[/tex]
This time is very small in years
Convert to minutes
[tex]1.58*10^{-5} \ years=1.58*10^{-5} (365)(24)(60)=8.3\ min[/tex]
step 2
Find the time it takes for the spaceship to travel from the Sun to Alpha Centaur
The distance from the the Sun to Alpha Centaur is equal to
[tex]2.5*10^{13}\ miles[/tex]
The spaceship can travel at the speed of light
The light can travel a distance of [tex]5.88*10^{12}\ miles[/tex] in a year
so
using a proportion
[tex]\frac{5.88*10^{12}\ miles}{1\ year}=\frac{2.5*10^{13}\ miles}{x}\\\\x=(2.5*10^{13})/5.88*10^{12}\\\\x=4.25\ years[/tex]
[tex]4.25\ years< 5\ years[/tex]
therefore
The spaceship will get to Alpha Centaur in time
