Final answer:
The magnitude of the driver's resultant displacement is approximately 5.03 km, and the direction is approximately 20.2° north of west. This is determined by calculating the components of displacement in the north-south and east-west directions and then using the Pythagorean theorem and the arctangent function for magnitude and direction, respectively.
Step-by-step explanation:
To find the magnitude and direction of the resultant displacement for a driver who drives 3.25 km north, 4.75 km west, and 1.5 km south, we will use the method of components.
Firstly, we define a coordinate system with north as the positive y-direction and east as the positive x-direction. The driver's movements can be broken down as follows:
North movement: +3.25 km
West movement: -4.75 km
South movement: -1.5 km
Calculating the total movement in the y-direction (north-south axis):
Total north-south displacement (y-component): 3.25 km - 1.5 km = 1.75 km north
Since the driver did not move in the east direction, the x-component (east-west axis) is simply:
Total east-west displacement (x-component): -4.75 km west
Now, to find the resultant displacement, we use the Pythagorean theorem:
Resultant displacement magnitude = √((1.75 km)2 + (-4.75 km)2)
The magnitude of the resultant displacement is approximately 5.03 km.
For the direction, we find the angle using the tangent function:
tan(θ) = opposite/adjacent = 1.75/-4.75
θ = arctan(1.75/-4.75) ≈ -20.2° (measured from the negative x-axis, or west, towards the positive y-axis, or north)
Therefore, the direction of the resultant displacement is approximately 20.2° north of the west.