Reaching the Moon in 0.9 Seconds: A Physics Challenge

[iPhysics]

Homework Statement

Nothing travels faster than light, which manages to get to the moon from the Earth in 1 second. However, we can still get there in a shorter amount of time. How fast would we have to travel to reach the moon in 0.9 seconds?

Homework Equations

I know the question is weird but it's in my textbook. I'm confused to what formula to use, I was thinking perhaps the formula for time dilation? t= t0/sqroot of (1-v^2/c^2) ?

The Attempt at a Solution

I put 0.9 as t0 and t = 1 and calculated v, but my answer is smaller than the speed of light, and shouldn't it be larger since the question states that we get to the moon in a shorter amount of time? I'm not even sure if I'm doing this correctly because it's in the advanced section of my book. Any kind of help would mean a lot to me!

 

[adjacent]

Which grade are you studying?

 

[HallsofIvy]

No, the problem told you that "nothing travels faster than light" so the answer must be smaller than the speed of light. The point is that traveling slower than the speed of light, the time to the moon, relative to a person stationary with respect to the Earth and moon, would be larger than 1 second, but relative to a person moving, less than one second.

 

[iPhysics]

@adjacent I'm in 11th grade, which is almost the equivalent to sophomore year.

@HallsofIvy Oh I see. But is the formula correct? The answer I got after putting in the different values was v = 130766968,3 m/s, could that be correct? I'm sorry, physics isn't really my forte at the moment, especially the theory of relativity.