$\"\"$

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An airplane has an airspeed of $\"\"$ bearing $\"\"$ .

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Therefore, the velocity of the airplane relative to the air is $\"\"$ .

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$\"\"$

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$\"\"$

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$\"\"$ .

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The velocity of the wind $\"\"$ has magnitude $\"\"$ bearing $\"\"$ .

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Therefore, the wind velocity $\"\"$ in terms of $\"\"$ and $\"\"$ as $\"\"$

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$\"\"$

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$\"\"$ .

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$\"\"$

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Find the velocity of the plane relative to the ground.

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The velocity of the plane relative to the ground $\"\"$ is $\"\"$ .

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Substitute $\"\"$ and $\"\"$ .

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$\"\"$

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$\"\"$ .

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$\"\"$

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Find the actual speed and direction of the plane relative to the ground.

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The velocity relative to the ground is $\"\"$ .

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\

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The standard form of the vector is $\"\"$ .

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Compare the vector with general form.

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$\"\"$ .

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\

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Magnitude of the vector $\"\"$ is $\"\"$ .

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$\"\"$

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$\"\"$

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\

\

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$\"\"$

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The direction angle is $\"\"$ .

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Substitute $\"\"$ .

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$\"\"$

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$\"\"$

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The angle is $\"\"$ .

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Therefore, the direction angle is $\"\"$ .

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$\"\"$

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The vector path of the plane relative to the ground is $\"\"$ .

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\

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The ground speed of the plane is $\"\"$

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The direction angle is $\"\"$ .