Because of a Storm, Ground Controllers Instruct the Pilot of a Plane

Multiple Choice

Because of a storm, ground controllers instruct the pilot of a plane flying at an altitude of 1.6 miles to make a $90^{\circ}$ turn and climb to an altitude of 1.8 miles. The model for the path of the plane during this maneuver is $\mathbf { r } ( t ) = \langle 4 \cos 4 \pi t , 4 \sin 4 \pi t , 1.6 + 1.6 t \rangle , 0 \leq t \leq \frac { 1 } { 8 } \text { where } t \text { is the }$ time in hours and is the distance in miles. Determine the speed of the plane. Round your answer to The nearest integer.

A) 50 mi/h
B) 16 mi/h
C) 54 mi/h
D) 34 mi/h
E) 79 mi/h