Answer:
a) To solve graphically, we will draw a vector diagram where the vectors A, B, and C are drawn to scale and in the correct direction. The sum of these vectors will be the resultant vector.
We can start by drawing vector A as a line segment 2 units long in the direction of MNW. Then, we draw vector B as a line segment 4 units long in the direction north of east. Finally, we draw vector C as a line segment 7 units long in the direction due south.
Next, we will add vector B to the head of vector A. Starting at the tail of vector A, we draw a line segment 4 units long in the direction north of east. The head of this line segment is the head of vector B.
Finally, we will add vector C to the tail of the resultant of vectors A and B. Starting at the tail of the resultant of vectors A and B, we draw a line segment 7 units long in the direction due south. The head of this line segment is the head of vector C.
The resultant vector is the vector that starts at the tail of vector A and ends at the head of vector C. We can measure the magnitude and direction of the resultant vector using a ruler and protractor.
b) To solve analytically, we will use vector addition. We can write each vector in terms of its x and y components.
A = 2MNW = (0, 2)
B = 4m north of east = (4cos(45), 4sin(45)) = (2.83, 2.83)
C = 7m due south = (0, -7)
To find the resultant vector, we add the x components and the y components separately.
Rx = 0 + 2.83 + 0 = 2.83
Ry = 2 + 2.83 - 7 = -2.17
Therefore, the resultant vector is R = (2.83, -2.17). We can find the magnitude and direction of the resultant vector using the Pythagorean theorem and trigonometry.
|R| = sqrt(2.83^2 + (-2.17)^2) = 3.56
θ = arctan(-2.17/2.83) = -38.9 degrees
Therefore, the magnitude of the resultant vector is 3.56 m and the direction