An airplane flies due north at 225 km/h relative to the air. There is a wind blowing at 60 km/h to the northeast relative to the ground. What are the plane's speed and direction relative to the ground?

270.78 m/s and 9 degrees north of east

Explanation:

Suppose that the wind direction is 45 degree relative to the eastern direction. Let east and north be the positive horizontal () and vertical () directions here. We can calculate the horizontal and vertical components of wind velocity

The velocity of the wind can be rewritten as the following

The velocity of the airplane that is 225 km/h due north is

The plane velocity relative to the ground is its velocity relative to the wind plus the wind velocity relative to the ground

The magnitude and direction of this velocity vector can be calculated

 north of east

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distance = 150m

displ = root (50 ^2 + 100^2)

root(2500+10000)

root 125000