An airplane, traveling with a constant engine speed, makes a large and perfect circle parallel to the ground. There is no wind. Will it complete the same circle in greater, less or the same time if there is a wind of constant speed and direction, assuming that the plane travels with the same constant engine speed that it had before?
For exactly half of the circular path the wind boosts the airplane’s ground speed and for the other half of the path the wind slows it. There is a temptation to suppose that these forces balance each other, with the result that the airplane’s time for the entire circle is the same as if there were no wind. This is not the case, because the time during which the plane’s speed is boosted is obviously shorter than the time during which it is slowed, with the result that the total time in the wind is greater than if there were no wind. (For a rigorous proof by way of calculus, see the American Mathematical Monthly, December 1945; page 584.)
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A version of this puzzle originally appeared in the February 1960 issue of Scientific American.