Final answer:
a) The angle in polar coordinates is 30°. b) The North/South and East/West components of the displacement are 433.01m and 250m, respectively.
Step-by-step explanation:
a) In polar coordinates, the angle of a straight line can be measured from the positive x-axis in a counterclockwise direction. Given that the duck is flying 60° N of W, we need to determine the angle in polar coordinates. To do this, we subtract the given angle from 90° (since it is north of the west direction). Therefore, the angle in polar coordinates is 90° - 60° = 30°.
b) To find the North/South and East/West components of the displacement, we use the trigonometric functions sine and cosine. The North/South component can be found by multiplying the displacement by the sine of the angle, and the East/West component can be found by multiplying the displacement by the cosine of the angle.
The North/South component = 500m × sin(60°) = 433.01m.
The East/West component = 500m × cos(60°) = 250m.