# Airplane landing path

#### wisredz

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

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#### wisredz

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...

#### himanshu121

now at the top and bottom it is flat so dy/dx at x=0 and x=-L should be zero,

#### himanshu121

oh u posted again,
$$y= ax^3+bx^2+cx$$
on Solving u will have c=0
Therefore
$$y= ax^3+bx^2$$
u can get values of a and b from
dy/dx at x= -L, is zero
and also y(-L) = H

#### wisredz

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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