Question

32. Vectors A, having magnitude 2.5m pointing 37∘South of east and B having magnitude 3.5m pointing 30∘north of east are added. What is the magnitude of the resultant vector? A.1m B.5.03m C.5.9m D.6.5m

Answer 1

Compute components:
- Ax = 2.5 cos37° = 2.5(0.7986) = 1.997 m
- Ay = −2.5 sin37° = −2.5(0.6018) = −1.505 m
- Bx = 3.5 cos30° = 3.5(0.8660) = 3.031 m
- By = 3.5 sin30° = 3.5(0.5) = 1.750 m

Resultant:
- Rx = 1.997 + 3.031 = 5.028 m
- Ry = −1.505 + 1.750 = 0.245 m

Magnitude = sqrt(Rx^2 + Ry^2) = sqrt(5.028^2 + 0.245^2) ≈ 5.03 m.

Answer: B. 5.03 m.