The following are information to solve questions 1 and 2.

An approach path for an aircraft landing is shown in the below figure that has the following conditions:

I) The cruising altitude is h when descent starts at a horizontal distance L from touch down at the origin

II) The pilot maintains a constant horizontal speed v throughout the descent

III) The absolute value for the vertical acceleration won't exceed constant k that is much less than the acceleration that is due to gravity

1. For the first question find a cubic polynomial P(x)=ax^3+bx^2+cx+d that satisfies the first condition (I) by imposing suitable conditions for P(x) and P'(x) at the start of the descent and at touchdown.
2. For this question use the conditions ii and iii to show that (6hv^2/L^2) less than or equal to k