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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:

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Robert Howard
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confused
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1 Answers1

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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!

Dmoreno
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  • you can use a derivative equation to solve for a & b?

    ... really...

     – confused Jan 20 '14 at 00:36
  • Hi there again. Yes, indeed you can, but notice that if you compute the first derivative and evaluate it in some fixed $x$ position, say $x^$, then $y'(x^) = y'(x^;a,b)$ is then a function of $a$ and $b$, exclusively (likewise for $y(x^;a,b)$). – Dmoreno Jan 20 '14 at 00:41
  • i see... cool, ill be sure to think of this for future questions.

    Thank you! :)

     – confused Jan 20 '14 at 00:43
  • You're welcome. Good luck! – Dmoreno Jan 20 '14 at 00:45