To find the magnitude and direction of the total movement of the driver, we can use the Pythagorean theorem and trigonometric functions.
1) Magnitude:
The magnitude represents the total distance traveled by the driver. We can determine this by calculating the hypotenuse of a right triangle formed by the two legs of the journey (west and south).
Using the Pythagorean theorem, we have:
magnitude = √(west^2 + south^2)
Given that the driver drove 14 km to the west (negative x-axis direction) and then 44 km to the south (negative y-axis direction), we have:
west = -14 km
south = -44 km
Substituting the values into the formula:
magnitude = √((-14)^2 + (-44)^2)
= √(196 + 1936)
= √(2132)
≈ 46.17 km
So, the magnitude of the total movement of the driver is approximately 46.17 km.
2) Direction:
To find the direction, we need to calculate the angle measured counterclockwise from the positive x-axis. We can use the inverse tangent function (tan^(-1)) to find the angle between the resultant vector and the positive x-axis.
Direction = tan^(-1)(south/west)
Using the given values:
Direction = tan^(-1)(-44/-14)
= tan^(-1)(44/14)
≈ 71.56°
So, the direction of the total movement of the driver is approximately 71.56° counterclockwise from the positive x-axis.