## Calculus: Approach ath for a plane.

An approach path for an aircraft landing satisfies the following conditions:
(i)The cruising altitude is h when descent starts at a horizontal distance l from touchdown at the origin.

(ii) The pilot must miantain a constant horizontal speed v throughout descent.

(iii) The absolute value of th vertical acceleration should not exceed a constant k (which is much less than the acceleration due to gravity).

a. FInd a cubic polynomial P(x) = ax^3 + bx^2 + cx + d that satisfies condition (i) by imposing suitable conditions on P(x) at the start of descent and at touchdown.

b. use conditions (ii) and (iii) to show that 6hv^2 / l^2 is less than or equal to k.

c. Suppose that an airline decides not to allow vertical acceleration of a plane exceed k = 860 mi/hr^2. If the cruising altitude of a plane is 35,000 feet and the speed is 300 mi/hr how far away from the airport should the pilot start descent?