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A plane is capable of flying at a speed of 180 km/h in still air. The...

A plane is capable of flying at a speed of 180 km/h in still air. The pilot takes off from an airfield and heads due north according to the planes compass. After 30 mins of flight time, the pilot notices that, due to the wind the plane has actually traveled 80km at an angle of 5 degrees east of north. What is the wind's velocity vector? Make a diagram, show step by step clearly and the reasoning of each step.

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