An approach path for an aircraft landing is shown in the figure and satisfies the following conditions:

( i ) The cruising altitude is when descent starts at a horizontal distance from touchdown at the origin.

( ii ) The pilot must maintain a constant horizontal speed throughout descent.

( iii ) The absolute value of the vertical acceleration should not exceed a constant (which is much less than the acceleration due to gravity).

- Find a cubic polynomial
P(x)=ax3+bx2+cx+dthat satisfies condition ( i) by imposing suitable conditions on P(x) and P'(x) at the start of descent and at touchdown.

WE know from the understanding of the graph that (0,0) is 1 point in the graph, so we can conclude thatd = 0

P′(x)=3ax2+2bx+c

I am not sure if we can substitute (0,0) here as well.

Using P'(0) = 0, we can easily see thatc=0.

So now we currently haveP(x)=ax3+bx2

Now if we take P'(l) = 0 then we get l=0 orl=−b3a2

How do we use this to get rid of theaandbin the equation?