$\"\"$

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The constant airspeed of Boeing 747 jumbo jet is $\"\"$ per hour headed due north.

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(a)

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Consider the direction north is along the positive $\"\"$ -axis.

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Therefore, the velocity of the 737 relative to the air is $\"\"$ .

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The velocity of the jet stream $\"\"$ has magnitude $\"\"$ in northeast direction.

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Hence the angle between the $\"\"$ and $\"\"$ is $\"\"$ .

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

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$\"\"$

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$\"\"$ .

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$\"\"$

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(b) Find the velocity of the 747 relative to the ground.

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The velocity of the 737 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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(c) Find the actual speed and direction of the 747 relative to the ground.

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

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

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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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(a) $\"\"$ and $\"\"$ .

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(b) $\"\"$

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(c) $\"\"$ and direction angle is $\"\"$ .