Chapter 12.4, Problem 65E

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

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

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?