Question

Solve the following for the components of each vector:

Vectors:
A = 35 km at 25° N of E
B = 15 km at 10° W of N
C = 20 km at 43° S of W
D = 40 km at 28° S of E

Answer 1

To find the components of each vector, use trigonometry to find the North and East components. For each vector, multiply the magnitude of the vector by the sine or cosine of the appropriate angle. For example, for vector A, the North-component is found by multiplying the magnitude of A by the sine of the angle.

Step-by-step explanation:

To solve for the components of each vector, we need to separate them into their North and East components. Here are the steps:

1. For vector A: North-component = A * sin(angle) = 35 km * sin(25°) = 14.35 km; East-component = A * cos(angle) = 35 km * cos(25°) = 31.35 km;
2. For vector B: North-component = B * cos(angle) = 15 km * cos(10°) = 14.54 km; East-component = B * sin(angle) = 15 km * sin(10°) = 2.59 km;
3. For vector C: North-component = -C * sin(angle) = -20 km * sin(43°) = -13.38 km; East-component = C * cos(angle) = 20 km * cos(43°) = 14.25 km;
4. For vector D: North-component = -D * sin(angle) = -40 km * sin(28°) = -19.15 km; East-component = -D * cos(angle) = -40 km * cos(28°) = -34.81 km;