Question

17. A glider lands 26 miles west and 12 miles south from where it took off. The result of the trip
can be described by the vector (-26, -12).
What is another description of this vector using distance (for magnitude) and direction?

about 29 miles at 25° south of west
about 25 miles at 29° south of east
about 29 miles at 25° south of east
about 25 miles at 29° south of west

Answer 1

By finding the magnitude and bearing, we conclude that the correct option is:

"about 29 miles at 25° south of west"

How to write the vector in polar coordinates?

For a vector (x, y), the polar coordinates are the magnitude R and the bearing θ.

Such that:

$R = \sqrt{x^2 + y^2} \\\\\theta = Atan(y/x)$

In this case, the original vector is (-26, -12), replacing that we get:

$R = \sqrt{(-26)^2 + (-12)^2} = 28.6 \\\\\theta = Atan(-12/-26) = 24.7\°$

Where the angle is measured from the negative x-axis counterclockwise, so it is South of West.

Then we can describe this vector as:

"About 29 miles at 25° south of west".

The first option is the correct one.

If you want to learn more about vectors:

https://brainly.com/question/3184914

#SPJ1