Worded Problem: Model a Plane Landing

Question

I have no idea to model this. All I know are the two points $(50, 10)$ and $(0,0)$ Then from after solving I get $a=1/12500$ and $b=0$

The textbook answers are:

Answer 1

The key is the word "smoothly" so this means that the plane should start the landing with zero-derivative (no slope) along the $x$ coordinate in its trajectory, so $y'(x)=0$ when $x = 50 \, km$.

Take this into account and notice that $y(0) = 0$ is always satisfied, no matter what the values of $a$ and $b$ are. Plug this information to your problem ($y(50)=10, \ y'(50) = 0$) and you will have:

$$a = -\frac{1}{6250} \wedge b = 75,$$

when $x$ is measured in $km$.

Cheers!