Chapter 3, Problem 14PS

(a)

To determine

To calculate: The following table for an airplane that has a speed of $‖v‖=100\text{miles per hour}$,

$\begin{array}{lllllll}\theta \hfill & 0.5°\hfill & 1.0°\hfill & 1.5°\hfill & 2.0°\hfill & 2.5°\hfill & 3.0°\hfill \\ ‖v‖\sin \theta \hfill & \hfill & \hfill & \hfill & \hfill & \hfill & \hfill \\ ‖v‖\cos \theta \hfill & \hfill & \hfill & \hfill & \hfill & \hfill & \hfill \end{array}$

Where $v$ is velocity of airplane, $‖v‖\sin \theta$ is vertical and $‖v‖\cos \theta$ is horizontal components of the velocity $v$.

(b)

To determine

Whether speed of the airplane is equal to the sum of vertical and horizontal components of its velocity or not. If not, then determine the method to find the speed of an airplane whose velocity components were known.

(c)

To determine

To calculate: The speed of an airplane with the given velocity components,

$\begin{array}{c}\left(\text{i}\right)‖v‖\sin \theta =5.235\text{miles per hour}\\ ‖v‖\cos \theta =149.909\text{miles per hour}\\ \\ \left(\text{ii}\right)‖v‖\sin \theta =10.463\text{miles per hour}\\ ‖v‖\cos \theta =149.634\text{miles per hour}\end{array}$

Where $v$ is velocity of airplane, $‖v‖\sin \theta$ is vertical component and $‖v‖\cos \theta$ is horizontal component of velocity of airplane.