Final answer:
To calculate the magnitude and direction of the resultant vector, we sum the x and y components of the given vectors and then use the Pythagorean theorem and trigonometry to find the magnitude (≈ 8.49 units) and angle (approximately 19.29° North of West).
Step-by-step explanation:
To find the magnitude and direction of the resultant vector, we need to break down the vectors into their components and then use vector addition.
Vector Components
Vector A is 5.0 units towards west, which we can consider as -5.0 units on the x-axis. Vector B is 8.0 units south, which we can consider as -8.0 units on the y-axis (since south is typically considered negative in coordinate systems).
For the vector of 6.0 magnitude with a 60-degree angle towards NW (assuming MW implies northwest), we have to decompose it into x and y components using trigonometric functions:
X component (6.0 * cos(60°)) = 3.0 units towards west
Y component (6.0 * sin(60°)) = 5.20 units towards north
Now, let's combine these components:
Total x component = -5.0 (west) + 3.0 (west)
= -8.0 units
Total y component = -8.0 (south) + 5.20 (north)
= -2.8 units
Resultant Vector
The next step is to calculate the magnitude (√(x² + y²)) and direction (tan-1(y/x)) of the resultant vector.
Therefore:
Magnitude: √((-8.0)² + (-2.8)²) ≈ 8.49 units
Direction: tan-1(-2.8 / -8.0) ≈ 19.29° North of West