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.


$\begin{equation} \begin{aligned} s =& \sqrt{1+d^2}; && d = 350 t\\ s =& \sqrt{1+(350t)^2}\\ s =& \sqrt{1+122500t^2} \end{aligned} \end{equation}$