Chapter 8.7, Problem 26PPS

To determine

To calculation:

Resultant velocity and direction of watercraft according to observer.

Answer to Problem 26PPS

Resultant velocity is $15.13m/s$ and direction of watercraft according to observer is $352.41°$ .

Explanation of Solution

Given information:

  

Calculation:

Resultant vector is as below:

Resultant vector is that starts at the beginning o the velocity vector and ends at the tip of the arrowhead of the current.

  

Now use Pythagoras theorem to find the resulting vector magnitude.

  $\begin{array}{l}\overrightarrow{r}=\sqrt{{15}^2+2^2}\\ \overrightarrow{r}=\sqrt{225+4}\\ \overrightarrow{r}=\sqrt{229}\\ \overrightarrow{r}=15.13m/s\end{array}$

To find vector direction use trigonometry,

  $\begin{array}{l}\tan \theta =\frac{opp}{adj}\\ \tan \theta =\frac{2}{15}\end{array}$

Take the inverse of tangent,

  $\begin{array}{l}\theta ={\tan }^{-1}\left(\frac{2}{15}\right)\\ \theta =7.59°westofnorth\end{array}$

Since compass directions start with $0°$ as north and go clockwise until get back to $360°$ as north. Subtract angle from $360$ to get true compass heading.

  $360-7.59=352.41°$

Hence, Resultant velocity and direction of watercraft according to observer is $15.13m/s$ and $352.41°$ respectively.