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A person swims 6.4 meters per

second north while being

pushed by a current moving

west at 2.1 meters per second.

What is the angle of the

swimmer's resultant vector?

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

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