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.

 

[HalfLostAndSearching]

I can provide a response to this content by explaining the concept of time dilation and why your calculated velocity may be smaller than the speed of light.

According to Einstein's theory of relativity, time dilation occurs when an object moves at speeds close to the speed of light. This means that time appears to pass slower for the moving object compared to a stationary observer. In other words, the faster an object moves, the slower time appears to pass for that object.

In this scenario, if we were to travel to the moon in 0.9 seconds, we would need to travel at a velocity close to the speed of light. This means that time would appear to pass slower for us, and therefore, 0.9 seconds for us would be equivalent to 1 second for a stationary observer on Earth.

The formula you have mentioned, t= t0/sqrt(1-v^2/c^2), is the correct formula for time dilation. However, it is important to note that this formula only applies to objects moving at constant velocities. In this scenario, we are not given a specific velocity, so it is not possible to calculate the exact speed required to reach the moon in 0.9 seconds.

Additionally, even if we were able to calculate the exact velocity, it is possible that it may be smaller than the speed of light. This is because the speed of light is the maximum speed at which anything can travel in the universe. It is not possible to travel at a speed faster than the speed of light.

In conclusion, the concept of time dilation explains why it is not possible to reach the moon in 0.9 seconds, as it would require us to travel at a velocity close to the speed of light. And even if we were able to achieve such a velocity, it would still be smaller than the speed of light. I hope this explanation helps to clarify your confusion.