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Approach trajectory of a plane.

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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.
(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 acce1eration 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

....
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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