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Question Number 16281 by Tinkutara last updated on 20/Jun/17
A plane moves in windy weather due  east while the pilot points the plane  somewhat south of east. The wind is  blowing at 50 km/hr directed 30° east  of north, while the plane moves at 200  km/hr relative to the wind. What is  the velocity of the plane relative to the  ground and what is the direction in  which the pilot points the plane?
$$\mathrm{A}\:\mathrm{plane}\:\mathrm{moves}\:\mathrm{in}\:\mathrm{windy}\:\mathrm{weather}\:\mathrm{due} \\ $$$$\mathrm{east}\:\mathrm{while}\:\mathrm{the}\:\mathrm{pilot}\:\mathrm{points}\:\mathrm{the}\:\mathrm{plane} \\ $$$$\mathrm{somewhat}\:\mathrm{south}\:\mathrm{of}\:\mathrm{east}.\:\mathrm{The}\:\mathrm{wind}\:\mathrm{is} \\ $$$$\mathrm{blowing}\:\mathrm{at}\:\mathrm{50}\:\mathrm{km}/\mathrm{hr}\:\mathrm{directed}\:\mathrm{30}°\:\mathrm{east} \\ $$$$\mathrm{of}\:\mathrm{north},\:\mathrm{while}\:\mathrm{the}\:\mathrm{plane}\:\mathrm{moves}\:\mathrm{at}\:\mathrm{200} \\ $$$$\mathrm{km}/\mathrm{hr}\:\mathrm{relative}\:\mathrm{to}\:\mathrm{the}\:\mathrm{wind}.\:\mathrm{What}\:\mathrm{is} \\ $$$$\mathrm{the}\:\mathrm{velocity}\:\mathrm{of}\:\mathrm{the}\:\mathrm{plane}\:\mathrm{relative}\:\mathrm{to}\:\mathrm{the} \\ $$$$\mathrm{ground}\:\mathrm{and}\:\mathrm{what}\:\mathrm{is}\:\mathrm{the}\:\mathrm{direction}\:\mathrm{in} \\ $$$$\mathrm{which}\:\mathrm{the}\:\mathrm{pilot}\:\mathrm{points}\:\mathrm{the}\:\mathrm{plane}? \\ $$

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