Vector A has a magnitude of 5.00 and is at an angle of 36.9° south of east. Vector B has a magnitude of 6.40 and is at an angle of 20.0° west of north. Choose the positive x-direction to the east and the positive y-direction to the north.

Find the components of Vector A:

A. $ A_x = 5.00 \cos(36.9°), A_y = 5.00 \sin(36.9°) $

B. $ A_x = 5.00 \sin(36.9°), A_y = 5.00 \cos(36.9°) $

C. $ A_x = 5.00 \cos(20.0°), A_y = 5.00 \sin(20.0°) $

D. $ A_x = 5.00 \sin(20.0°), A_y = 5.00 \cos(20.0°) $

The components of vector A are calculated as Ax = 5.00 cos(36.9°) and Ay = 5.00 sin(36.9°). Since the vector is south of east, Ax is positive and Ay is negative.

Explanation:

In breaking down vector components into their horizontal (x-axis) and vertical (y-axis) parts, we use trigonometric relationships. For vector A which has a magnitude of 5.00 and is at an angle of 36.9° south of east, we can calculate its components using the cosine for the x-component and sine for the y-component.

Thus, the components of vector A would be: Ax = 5.00 cos(36.9°), Ay = 5.00 sin(36.9°). But because the vector is south of east, in terms of direction, Ax will be positive (east), and Ay will be negative (south).

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