Single Variable Calculus, Chapter 1, 1.3, Section 1.3, Problem 56

Assume that an airplane is flying at a speed of $350mi/h$ at an altitude of one mile and passes directly over a radar station at time $t = 0$.



(a) We need to express the horizontal distance $d$ (in miles) that the plane has flown as a function of $t$,

$d = 350 t$

(b) Then express the distance $s$ between the plane and the radar station as a function of $d$,



$
\begin{equation}
\begin{aligned}

s^2 =& 1^2 + d^2\\
s =& \sqrt{1+d^2}

\end{aligned}
\end{equation}
$






(c) And express $s$ as a function of $t$ using composition.


$
\begin{equation}
\begin{aligned}

s =& \sqrt{1+d^2}; && d = 350 t\\
s =& \sqrt{1+(350t)^2}\\
s =& \sqrt{1+122500t^2}

\end{aligned}
\end{equation}
$