WHERE SHOULD A PILOT START DESCENT?
An approach path for an aircraft landing is shown in the figure and satisfies the following
(i) The cruising altitude is h when descent starts at a horizontal distance e from
touchdown at the origin.
(ii) The pilot must maintain a constant horizontal speed v throughout descent.
(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
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
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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