Latitude of Flight

Take the circumference of the earth at the equator to be 24,000 miles. An airplane taking off at the equator and flying west at 1000 miles an hour would land at exactly the same time that it started (why?). Moreover, the sun would not move in the plane’s sky during the flight. (Work this out visually in your mind.) Now, at what degree of latitude could a plane flying 500 miles per hour keep up with the sun in this way?

Show/Hide Solution

We want x°. To begin we want our plane to fly in a circle whose circumference is 500 miles/hour x 24 hours = 12000 miles.

The radius of that circle is y.
2piy = 12000y = 12000/2pi = 6000/pi ≈ 1910 miles.

Then, over here, we use r = radius of the earth = 12000/pi, and cos x = y/r = (6000/pi) / (12000/pi) = 1/2. Thus x° = 60°.

60° latitude is either at about Southern Alaska or Tierra del Fuego.

Leave a Reply

Your email address will not be published. Required fields are marked *