Final answer:
To find the western component of a displacement vector, trigonometric functions like sine and cosine are used to decompose the vector into east-west and north-south components. Western direction is considered negative on the east-west axis but represented as positive when calculating the magnitude of the western component alone.
Step-by-step explanation:
Finding the western component of a displacement vector involves using trigonometric functions to decompose the vector into its respective components along the north-south and east-west axes. For an initial example, if a person has a total displacement of 10.3 blocks in a direction 29.0° north of east, the displacement in the eastern and northern directions can be found using the cosine and sine functions, respectively. However, to find the component that is west of north, adjustments need to be made because western directions represent the negative direction along the east-west axis. Assuming another scenario where a vector displacement is given as 32.0 km at 35.0° south of west, to find the displacement south and west, one would utilize the sine and cosine functions: south component = 32.0 km * sin(35.0°) and west component = 32.0 km * cos(35.0°), with the understanding that west direction will be represented as a positive value.