Plane Speed = f(Latitude)

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 1,000 miles per hour would land at exactly the same time that it started, and the sun would not move in the plane’s sky during that flight. (Work this out visually in your mind.) Now, can you find a formula so that the speed of a plane flying at any particular latitude and keeping up with the sun, is a function of that latitude: speed = f(x°)?

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This problem is similar to #4220.21 in Stella Set #8; we’ll use the sketches from its solution.

The task is to find the speed of the plane, given its latitude of x°.

Given the circumference of the earth, we can determine the radius.

This checks out when the plane is at the equator (x = 0°) or at the north pole (x = 90°). Pretty cool formula.

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