Respuesta :
Using the slope concept, it is found that the angle of the swimmer's resultant vector is of 71.83º.
What is a slope?
- The slope is given by the vertical change divided by the horizontal change.
- It's also the tangent of the angle of depression.
In this problem:
- The person swims 6.4 meters per second north, hence the vertical change is of 6.4.
- The person is being pushed by a current moving west at 2.1 meters per second, hence the horizontal change is 2.1.
Then, considering that the slope is the tangent of the angle of depression [tex]\theta[/tex], which is also the angle of the swimmer's resultant vector, we have that:
[tex]\tan{\theta} = \frac{6.4}{2.1}[/tex]
[tex]\tan{\theta} = 3.04761904762[/tex]
Using a trigonometric calculator:
[tex]\arctan{\tan{\theta}} = \arctan{3.04761904762}[/tex]
[tex]\theta = 71.83^{\circ}[/tex]
The angle of the swimmer's resultant vector is of 71.83º.
You can learn more about the slope concept at https://brainly.com/question/26125945
