Chapter 12.4, Problem 61E

Air Traffic Control

Because of a storm, ground controllers instruct the pilot of a plane flying at an altitude of 4 miles to make a 90°ï¿½ turn and climb to an altitude of 4.2 miles. The model for the path of the plane during this maneuver is

$\begin{array}{cc}r(t)=\langle 10\cos 10\pi t,10\sin 10\pi t,4+4t\rangle ,& 0\le t\le \frac{1}{20}\end{array}$

where t is the time in hours and r is the distance in miles.

(a) Determine the speed of the plane.

(b) Calculate $a_T$ and a_N. Why is one of these equal to 0?