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? (use cos37∘=0.8,sin37∘=0.6,cos30∘=0.87,sin30∘=0.5)
A.1m B.5.03m C.5.9m D.6.5m

Answer 1

Break into components (east = +x, north = +y).

A: Ax = 2.5 cos37 = 2.5(0.8) = 2.00 m
Ay = −2.5 sin37 = −2.5(0.6) = −1.50 m

B: Bx = 3.5 cos30 = 3.5(0.87) = 3.045 m
By = 3.5 sin30 = 3.5(0.5) = 1.75 m

Resultant: Rx = 2.00 + 3.045 = 5.045 m, Ry = −1.50 + 1.75 = 0.25 m

|R| = sqrt(Rx^2 + Ry^2) = sqrt(5.045^2 + 0.25^2) ≈ 5.05 m

Closest choice: B. 5.03 m.