A position vector r has a magnitude of 22.5 m and a direction of 190 degrees with respect to the positive x-axis. Find its x-component and y-component.

1. Convert the angle to radians if necessary (not needed as most calculators can handle degrees directly).

2. Calculate the x-component using the cosine function:

r_x = 22.5 \cos(190^\circ)

r_x \approx 22.5 \times (-0.9397)

r_x\approx-22.2

3. Calculate the y-component using the sine function:

r_y = 22.5 \sin(190^\circ)

r_y \approx 22.5 \times (-0.3420)

r_y\approx-3.9\text{ }

Thus, the x-component and y-component of the position vector are approximately:

r_x\approx-22.2\text{ }

r_y\approx-3.9\text{ }