APPLIED PROJECT WHERE SHOULD A PILOT START DESCENT? An approach p...

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APPLIED PROJECT WHERE SHOULD A PILOT START DESCENT? An approach path for an aircraft landing is shown in the figure and satisfies the following - conditions: (i) The cruising altitude is h when descent starts at a horizontal distance e from touchdown at the origin. y=P(x) (ii) The pilot must maintain a constant horizontal speed v throughout descent. h (iii) The absolute value of the vertical acceleration should not exceed a constant k (which is much less than the acceleration due to gravity). 1. Find a cubic polynomial P(x) = ax³ + bx2 + cx + d that satisfies condition (i) by x l imposing suitable conditions on P(x) and P'(x) at the start of descent and at touchdown. 2. Use conditions (ii) and (iii) to show that 6hv² e2 < k 3. Suppose that an airline decides not to allow vertical acceleration of a plane to exceed k = 860 mi/h². If the cruising altitude of a plane is 35,000 ft and the speed is 300 mi/h, how far away from the airport should the pilot start descent? 4. Graph the approach path if the conditions stated in Problem 3 are satisfied.

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