ma014 - How Not to Land at Lake Tahoe! Richard Barshinger...

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How Not to Land at Lake Tahoe! Richard Barshinger The American Mathematical Monthly, May 1992, Volume 99, Number 5, pp. 453–455. T he following problem gives a simplified model of landing an airplane. It is adapted and extended from Trim [ 1 ] and is regularly presented in first semester calculus at my campus, where it is unanimously enjoyed and wins some converts to the methods of calculus. Problem. An aircraft landing approach pattern is shaped generally as in Figure 1 below. The following conditions are imposed: a) The cruising altitude is h when descent begins at a horizontal distance L from the airstrip. b) A constant horizontal airspeed U must be maintained throughout descent (somewhat unrealistic). c) At no time must the vertical component of acceleration exceed (in absolute value) some fixed constant k , where g is the acceleration constant for gravity; i.e., (English units). Model the plane’s approach path by means of a cubic polynomial, using a coordinate system with origin at the beginning of the runway, so that descent starts at the point in units of your choice. Impose suitable conditions at the beginning of descent and at touchdown. Discuss the implications of condition c) above, in the cases:
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ma014 - How Not to Land at Lake Tahoe! Richard Barshinger...

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