Answer:
to determine the direction of the pedestrian's resultant vector, we need to calculate the magnitude and angle of the vector.
Explanation:
To determine the direction of the pedestrian's resultant vector, we can use trigonometry.
1. Draw a diagram to represent the displacement of the pedestrian.
Start by drawing a line segment to represent the 7.4 kilometers westward displacement. Then, draw a perpendicular line segment to represent the 9.2 kilometers southward displacement.
2. Use the Pythagorean theorem to find the magnitude of the resultant vector.
The magnitude of the resultant vector can be found by calculating the square root of the sum of the squares of the individual displacements:
Magnitude = √(7.4^2 + 9.2^2)
3. Use trigonometry to find the angle or direction of the resultant vector.
The angle can be determined by taking the inverse tangent of the ratio of the vertical displacement to the horizontal displacement:
Angle = arctan(9.2/7.4)
4. Convert the angle to a compass direction.
The angle obtained in step 3 is the angle with respect to the positive x-axis. We can convert this angle to a compass direction by considering the quadrants in which the angle lies. For example, if the angle is between 0° and 90°, the compass direction would be south of west.
Therefore, to determine the direction of the pedestrian's resultant vector, we need to calculate the magnitude and angle of the vector.