Final answer:
The problem involves calculating the resultant displacement of a person walking two separate legs with specified directions and distances using vector addition. After finding the components of each leg of the walk, they are summed to obtain total displacement, and trigonometric functions are used to find the final distance and direction.
Step-by-step explanation:
The question is related to the concept of vector addition and the determination of the resultant displacement for a person walking in specified directions and distances. To solve this, you must first break down each leg of the walk into its horizontal (x-axis) and vertical (y-axis) components. The components can be found using trigonometry, specifically the sine and cosine functions for the given angles.
For the first leg of the walk, 12.5 m at 20° west of north, the x-component (horizontal) is found by multiplying the distance by the cosine of 20°, and the y-component (vertical) by multiplying the distance by the sine of 20°, considering the north and east directions positive. For the second leg, 24 m at 40° south of west, the x-component is the distance multiplied by the cosine of 40° (this time in the negative direction since it is to the west) and the y-component is the distance multiplied by the sine of 40° (also negative because it's to the south).
Once the components for both legs have been calculated, sum the horizontal components to get the total horizontal displacement and the vertical components for the total vertical displacement. The magnitude of the total displacement R can be calculated using the Pythagorean theorem from the resultant x and y components. The angle of the displacement vector can be found using the arctangent function of the ratio of the y-component to the x-component ensuring to adjust for the correct quadrant.