A boat driver travelling west at 5km/hr finds that the wind appears to blow from the south. On doubling it's speed, the wind appears to blow from the southwest. Find the magnitude and direction of the winds velocity.

wind blowing NW at 7 km/hr

Explanation:

As the boat driver senses only south wind when heading west at 5 km/hr

The wind must have a westward component of 5 km/hr

On doubling his speed to 10 km/hr, the wind now appears from the SW meaning that the CHANGE in westward velocity (10 - 5 = 5 km/hr) must be equal to the northward component of wind.

If the boat stopped, the wind would blow from the SE at

√(5² + 5²) = √50 km/hr or about 7 km/hr

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