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Pilot Descent Point, Derivatives

  1. Oct 12, 2012 #1
    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
  2. jcsd
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