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EXAMPLE 3Finding the True Direction of an Airplane

An airplane has an air speed of 400 km/h and is headed east. Find the true direction of the airplane relative to the ground if there is a northwesterly wind of 80 km/ h.

Solution This is the same situation from Example 8 of Section 10.3. There, we found the velocity of the airplane relative to the ground is vg=(400+402)i402j.

The angle θ between vg and the vector i (the positive x-axis) is given by cosθ=vgi

The true direction of the plane is approximately 7.07^\circ south of east. See Figure 37.