An aeroplane must fly 1000 km from A to B, where AB is 30° west of north. Wind blows due north at 20 m s⁻¹ and the plane's air-speed is 150 m s⁻¹. Which option correctly gives the required heading and approximate flight time?
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Question

An aeroplane must fly 1000 km from A to B, where AB is 30° west of north. Wind blows due north at 20 m s⁻¹ and the plane's air-speed is 150 m s⁻¹. Which option correctly gives the required heading and approximate flight time?

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G1 Physics · Accepted Answer

Resolve velocity perpendicular to AB. Wind has perpendicular component: 20 sin30° =10 m s⁻¹. For the resultant to lie along AB, the plane's air velocity must have equal opposite perpendicular component: 150 sinφ =10 sinφ =1/15. So the plane should head φ=sin⁻¹(1/15) west of AB. Ground speed along AB is vg =150cosφ +20cos30°. Using cosφ=√(1-1/225)=√224/15: vg =10√224 +10√3 m s⁻¹. Time: t =1000×1000 / vg ≈ 6000 s ≈100 min.