15) a) If we start from 0 o latitude and proceed in a westerly direction, we can

Question

15) a) If we start from 0o latitude and proceed in a westerly direction, we can let T(x) denote the temperature at the point x at any given time. Assuming that T is a continuous function of x, show that at any fixed time there are at least 2 diametrically opposite points on the equator that have the same temperature.

b) Does the result in part (a) hold for points lying on any circle on the earth's surface?

c) Does the result in part (a) hold for barometric pressure and for altidue above sea level?

Explanation / Answer

(a) We are starting from any point on the 0 degree latitude , hence proceeding in the westerly direction .

Let the point of start be x = 0° and we proceed till x = 180°.Since any point can be chosen to be our reference point hence we need to repeat the cycle from x = 180° to x = 360° so as to balance the symmetry.Therefore , there must be atleast two diametrically points on the circle which have same temperature.

(b) Yes , it is true for any circle on the earth's surface with the logic used in Part (a)

(c) Yes it hold for barometric pressure but not for altitude above sea level as other factors play an important role.

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