Question

Você é um comandante de uma espaçonave. Sua missão é chegar até Alfa Centauro em cinco anos. A distância do Sol até Alfa Centauro é de 2,5 x milhas. A distância da Terra ao Sol é de, aproximadamente, 9,3 x milhas. A sua espaçonave pode viajar a velocidade da luz. Você Sabe que a luz pode percorrer uma distância de 5,88 x milhas em um ano. Será que você consegue chegar a Alfa Centauro a tempo? Justifique.

Answer 1

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

$9.3*10^7\ miles$

The spaceship can travel  at the speed of light

The light can travel a distance of $5.88*10^{12}\ miles$ in a year

so

using a proportion

$\frac{5.88*10^{12}\ miles}{1\ year}=\frac{9.3*10^7\ miles}{x}\\\\x=(9.3*10^7)/5.88*10^{12}\\\\x=1.58*10^{-5} \ years$

This time is very small in years

Convert to minutes

$1.58*10^{-5} \ years=1.58*10^{-5} (365)(24)(60)=8.3\ min$

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

$2.5*10^{13}\ miles$

The spaceship can travel  at the speed of light

The light can travel a distance of $5.88*10^{12}\ miles$ in a year

so

using a proportion

$\frac{5.88*10^{12}\ miles}{1\ year}=\frac{2.5*10^{13}\ miles}{x}\\\\x=(2.5*10^{13})/5.88*10^{12}\\\\x=4.25\ years$

$4.25\ years< 5\ years$

therefore

The spaceship will get to Alpha Centaur in time