For my calculus class I'm working on a project, and one of the questions is regarding 'where should a pilot start descent'.

I came here hoping that somebody might be able to assist me with the mathematics that goes along with the problem. In addition to solving the problem I need to explain why.

The question is as follows:

An approach path for an aircraft landing must satisfy the following conditions.

given y=P(x)

(i) The cruising altitude is "h" when descent starts at a horizontal distance"l" 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)=ax*3 + bx*2 + cx + d (*3 and *2 are exponents, ax to the third, and bx squared but I have no idea how to type those) 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 6hv*2/l*2

3. Suppose that an airline decides not to allow vertical acceleration of a plane to exceed k=860 mi/h*2 (*2 is an exponent, in this case squared. If the crusiing 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?

Thanks for any and all help that you can provide.