# Homework Help: Pilot Descent Point, Derivatives

1. Oct 12, 2012

### brembo

1. The problem statement, all variables and given/known data

Where should the pilot start descent? The approach path for an aircraft should satisfy:
i) The cruising altitude is h when descent starts. At horizontal distance.
ii) The pilot must keep a constant horizontal velocity, Vx, throughout the decent.
iii)|αy|≤ K << g
k = constant
g = gravity
|αy| = vertical component of acceleration

1) Find a cubic polynomial
y = P(x) = ax3 + bx2 + cx + d that satisfies:
(i) on P(x) , P'(x) @ x = 0 , x = L

2) Use (i) , (ii) to show:
(6hVx2) / L2 ≤ k

2. Relevant equations
P(x) = ax^3 + bx^2 + cx + d
(6hVx^2) / L^2 ≤ k

3. The attempt at a solution

I was able to conclude that:

y(0) = P(0) = d = 0 → P(x) = ax3 + bx2 + cx
And @ x = L : P(L) = aL3 + bL2 + cL = y(L) = h

Thats all I was able to get so far. I am stuck. If you guys need anymore info on the question let me know and ill do my best to help out

Thanks!

Last edited: Oct 12, 2012