Question

In the not so distant future we can conceivably build a space ship that will travel 0.25 times the speed of light. How long would it take this ship to reach the Andromeda galaxy?

Answer 1

Answer: It would take 10.16 million years.

Step-by-step explanation:

Light travels at a speed
`c=299 792 458(m)/(s)`.

A light-year is the distance that light travels in vacuum in one year.

The Andromeda Galaxy is 2.54 million light-years from the Earth.

This means that

`c*(2.54million.years)=2.54million.light.years`

Let's say
`v` is the speed of the ship. Then

`v=(c)/(4)` ⇒
`c=4v`

So, we have:

`4v*(2.54million.years)=2.54million.light.years`

⇒
`v*4(2.54million.years)=2.54million.light.years`

⇒
`v*(10.16million.years)=2.54million.light.years`

So, at speed
`v`, it would need a time of 10.16 million years.