Chapter 14.2, Problem 1ST

To determine

To find: The magnitude of $2u+v$ and find the bearing to the nearest degree.

Answer to Problem 1ST

The magnitude is $15.9681$ and the bearing is $0.9369°$ .

Explanation of Solution

Given:

The bearing of $u$ is $37°$ and the magnitude of $5$ .

The bearing of $v$ is $125°$ and the magnitude of $6$ .

Calculation:

Considerbearing $u$ as,

  $\begin{array}{c}u=\left(5\cos 37°+i5\sin 37°\right)\\ =3.82-i3.21\end{array}$

Consider bearing $v$ as,

  $\begin{array}{c}v=\left(6\cos 125°+i6\sin 125°\right)\\ =4.72-i3.69\end{array}$

Then,

  $\begin{array}{c}2u+v=2\left(3.82-i3.21\right)+4.72-i3.69\\ =7.64-i6.42+4.72-i3.69\\ =7.64-i6.42+4.72-i3.69\\ =12.36-i10.11\end{array}$

Then, the magnitude is,

  $\begin{array}{c}\left|2u+v\right|=\sqrt{{\left(12.36\right)}^2+{\left(10.11\right)}^2}\\ =15.9681\end{array}$

The bearing is,

  $\begin{array}{c}\theta ={\tan }^{-1}\left(\frac{10.11}{12.36}\right)\\ =0.9369°\end{array}$