Resolving velocity into east and north components using trigonometry

Steps:

• Velocity magnitude v = 8.0 km/h at θ = 30° north of east.
• East component (adjacent to θ) = v cos θ = 8.0 × cos 30° = 8.0 × (√3/2) ≈ 6.9 km/h.
• North component (opposite to θ) = v sin θ = 8.0 × sin 30° = 8.0 × 0.5 = 4.0 km/h.
• Components are 6.9 km/h east and 4.0 km/h north.

Why B is correct:

• B matches the components from the definition of vector resolution, where east = v cos θ and north = v sin θ for θ measured from east.

Why the others are wrong:

• A: Equal 4.0 values imply 45° angle (tan⁻¹(1) = 45°), not 30°.
• C: 4.6 and 6.9 imply ~56° angle (tan⁻¹(6.9/4.6) ≈ 56°), incorrect for 30°.
• D: Reverses sine and cosine, assigning larger value to north instead of east.

Final answer: B