Math – Exercise 7 (Algebra)

Given

A boat drives (10 km/h) on a river (4 km/h).


Find

The steering angle of the boat to traverse the river orthogonally.


Solution


\(
\begin{array}{l}
v_{river} = \begin{pmatrix}4\\0\end{pmatrix},\ v_{route} = \begin{pmatrix}0\\10\end{pmatrix} \\
v_{boat} = v_{route} – v_{river} = \begin{pmatrix}-4\\10\end{pmatrix} \\
\tan(\angle{v_{boat}}) = \frac{-4}{10},\ \angle{v_{boat}} = \arctan(-0,4) \approx -21,8°
\end{array}
\)


Answer

\(\angle{v_{boat}} \approx -21,8°\)