$\"\"$

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(a)

\

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Find the speed of the airplan $\"\"$ s flight.

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Since the airplane is traveling due east with a speed of $\"\"$ miles per hour, the component form of the speed $\"\"$ is $\"\"$ .

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Use the magnitude and the direction of the wind $\"\"$ to write this vector in component form.

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Angle $\"\"$ is the direction angle that $\"\"$ makes with the positive $\"\"$ - axis.

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So,

\"\"

.

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Component form of a vector

\"\"

is $\"\"$ .

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$\"\"$

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$\"\"$ .

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$\"\"$

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Add the algebraic vectors representing $\"\"$ and $\"\"$ to find the resultant velocity, vector $\"\"$ .

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$\"\"$

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$\"\"$

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$\"\"$ .

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$\"\"$

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Find the magnitude of the resultant vector $\"\"$ .

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$\"\"$

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The speed of the airplane $\"\"$ s flight is about $\"\"$ .

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$\"\"$

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(b)

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Find the angle of the airplan $\"\"$ s flight.

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Find the resultant direction angle $\"\"$ .

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$\"\"$

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Since the resultanr vector $\"\"$ in quadrant IV, $\"\"$ .

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$\"\"$

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$\"\"$ .

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The angle of the airplane $\"\"$ s flight is about $\"\"$ .

\

\

$\"\"$

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(a)

\

The speed of the airplane $\"\"$ s flight is about $\"\"$ .

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(b)

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The angle of the airplane $\"\"$ s flight is about $\"\"$ .