Chapter 8.5, Problem 27E

a.

To determine

To find: the angle of the path of the sailboat.

Answer to Problem 27E

  $9.5°\text{ south of east}$

Explanation of Solution

Given information:

Sailboat is moving east at 18 mph.

Current is moving south at 3mph.

Calculation:

The sketch of the given situation is shown below.

  

The direction can be evaluated as follows:

  $\begin{array}{c}\tan \theta =\frac{3}{18}\\ \theta ={\tan }^{-1}\left(\frac{3}{18}\right)\\ ={\tan }^{-1}\left(\frac{1}{6}\right)\\ \approx 9.5°\text{ south of east}\end{array}$

Thus the angle of path of sailboat is $9.5°$ south of east.

b.

To determine

To find: the speed of sailboat with respect to the ocean floor.

Answer to Problem 27E

18.2 mph

Explanation of Solution

Given information:

Sailboat is moving east at 18 mph.

Current is moving south at 3mph.

The sketch of the given situation is shown below.

  

Calculation:

The speed of sail-boat can be evaluated by using Pythagoras theorem as shown below.

  $\begin{array}{c}s=\sqrt{{18}^2+3^2}\\ =\sqrt{324+9}\\ =\sqrt{333}\\ =18.2\text{ mph}\end{array}$

Thus the speed of sail-boat with respect to the ocean floor is 18.2 mph.