Vector Addition for Resultant Velocity

Steps:

• Aircraft velocity components: north = 800 cos θ km/h, east = 800 sin θ km/h.
• Wind velocity: west = 200 km/h (or -200 km/h east).
• For due north resultant, east component = 0: 800 sin θ - 200 = 0 → sin θ = 0.25 → θ ≈ 14°.
• Resultant magnitude = north component = 800 cos 14° ≈ 776 km/h ≈ 770 km/h.

Why A is correct:

• Satisfies vector addition rule where wind's westward component is exactly canceled by aircraft's eastward component for due north direction.

Why the others are wrong:

• B: Magnitude 820 km/h exceeds airspeed, impossible as wind reduces north component.
• C: θ=76° gives sin θ ≈0.97, east component ≈776 km/h, overshoots wind cancellation.
• D: Combines C's incorrect θ with B's impossible magnitude.

Final answer: A