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Airplane landing path

  1. Jun 19, 2005 #1
    Hi I have this question that is driving me mad any help is appreciated.

    An airplane is flying at altitude H when it begins its decent to an airport runway that is at horizontal ground distance L from the airplane. Assume that the landing path of the airplane is the graph of a cubic polynomial fuction y=ax^3+bx^2+cx+dwhere y(-L)=H and y(0)=0.

    (a) What is dy/dx at x=0?
    (b) What is dy/dx at x= -L?
    (c) Use the values for dy/dx at x=0 and x= -L together with y(0)=0 and y(-L)=H to show that

    y(x)=H[2(x/L)^3+3(x/L)^2]

    Anyhelp is appreciated. Thanks in advance
     
    Last edited: Jun 19, 2005
  2. jcsd
  3. Jun 19, 2005 #2
    Btw, that dy/dx at x=0 equals c and that dy/dx at -L equals 0 is clear to me. My problem is that I cannot use those informations...
     
  4. Jun 19, 2005 #3
    now at the top and bottom it is flat so dy/dx at x=0 and x=-L should be zero,
     
  5. Jun 19, 2005 #4
    oh u posted again,
    [tex] y= ax^3+bx^2+cx[/tex]
    on Solving u will have c=0
    Therefore
    [tex] y= ax^3+bx^2[/tex]
    u can get values of a and b from
    dy/dx at x= -L, is zero
    and also y(-L) = H
     
  6. Jun 20, 2005 #5
    God, it is that easy then... It was 2 in the morning here(Turkey) Thanks a lot, I was going out of my mind.
     
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