We usually do not realize that we live on a curved surface of the Earth. Conside

Question

We usually do not realize that we live on a curved surface of the Earth. Consider the following example.
The latitude of New York City is 4043 N, and its distance from the north pole is 5486 km. Suppose you
hop on an eastbound airplane from New York City. The airplane ies along the 4043 N latitude line;

i.e.,
the airplane maintains a constant distance from the north pole. What is the total distance travelled when
the airplane returns to New York City? Is it greater or less than the distance given by the circumference
formula 2r where r is the distance from the north pole?

Explanation / Answer

Since the surface of earth is a curved therefore we need to find the exact cirlce along which the place files. In this case the circle is of 4043 N latitude line. Radius for such a circle is given by R = 6400 Cos(4043). Where 6400 is radius of the earth. So R ~ 4902 km. Then one can calculate the value of total distance from the formula 2R. Since radius of circle is less than the distance give in the problem which is 5486km. Therefore the plane travels lesser distance from the circumfrence fromula using r = distance of newyork from north pole.

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