# What is the expected roundtrip travel time if a wind is present?

• Crazysah
In summary: These are not consistent.In summary, the conversation discusses the Michelson-Morley experiment in relation to the effect of wind on travel time for a pilot flying due east and back. The roundtrip time is affected by the speed of the wind and the pilot's airspeed. The essential difference between this situation and the experiment is that the experiment shows equal travel times for light, while in the pilot's case, the travel times are not equal due to the effect of wind. Calculations and explanations are also provided for finding the expected roundtrip travel time in different wind directions.
Crazysah

## Homework Statement

The Michelson-Morley experiment for a real wind (This is taken from Resnick and Halliday, Basic Concepts in Relativity (MacMillan, New York, 1992).
A pilot plans to fly due east from A to B and back again. If u is her airspeed (speed of plane with respect to the air) and if l is the distance between A and B, it is clear that her roundtrip time t — if there is no wind — will be 2l/u.
a) Suppose, however, that a steady wind of speed v blows from the west. What will the round trip travel time now be, expressed in terms of l, u, and v?
b) If the wind is from the south, explain how you would find the expected roundtrip travel time, again as a function of l, u, and v. (If you can find the travel time, do it!)
c) Note that these two travel times are not equal. Should they be? Did you make a mistake?
d) In the Michelson-Morley experiment, however, the experiment seems to show that (for arms of equal length) the travel times (and thus path lengths) for light are equal; otherwise these experimenters would have found a pattern shift when they rotated their experiment. What is the essential difference between these two situations?

## Homework Equations

Distance = speed x time.

## The Attempt at a Solution

I = u x 21/u
I/u = 1 x 21
21 = I/u

The problem is I'm completely drawing a blank. Any help would be appreciated.

Thanks,
Crazysah

Anyone have any clue on this one?

a) What is her speed relative to the ground as she's going from A to B? Use this to calculate the time from A to B. Then do the same for the trip from B to A.

b) She will have to "aim" the plane a little to the right (south) of her target (B) in order to end up flying along a straight line from A to B. Use the Pythagorean theorem to find her speed relative to the ground as she flies towards B along that line.

That's all I have time for right now. Going to bed.

Crazysah said:
I = u x 21/u
I/u = 1 x 21
21 = I/u
By the way, I don't know what you're doing here. What's I? Where did you get the number 21? Also (21u)/u=21, so your first equality says I=21, while the second and third say that I=21u.

## What is basic relativity?

Basic relativity is a scientific theory developed by Albert Einstein that explains how gravity affects the motion of objects in space. It is a fundamental concept in physics that helps us understand the universe on a large scale.

## What is the difference between special relativity and general relativity?

Special relativity deals with the laws of physics in inertial frames of reference, while general relativity extends these laws to non-inertial frames of reference, incorporating the effects of gravity.

## How does relativity affect our daily lives?

Relativity has a small but measurable impact on our daily lives. For example, it affects the accuracy of GPS systems and the timing of satellite communications. However, these effects are only noticeable in highly precise measurements.

## What is the space-time continuum?

The space-time continuum is a concept in relativity that combines the three dimensions of space (length, width, and height) with the dimension of time. It is a fundamental aspect of the theory and helps explain how objects move and interact in the universe.

## Is relativity proven?

Yes, relativity has been extensively tested and has been confirmed by numerous experiments and observations. It is considered one of the most successful theories in physics and has been used to make accurate predictions about the behavior of objects in the universe.

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