$\"\"$

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Force used by the student to pull the backpack is $\"\"$ .

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$\"\"$ .

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(a)

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Student exerts $\"\"$ to pull her backpack $\"\"$ .

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Work done is $\"\"$ .

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Magnitude of directed distance $\"\"$ .

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Find the angle of her force.

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Use projection formula for work.

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Projection formula for work: $\"\"$ .

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$\"\"$ .

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Substitute $\"\"$ , $\"\"$ and $\"\"$ in above expression.

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$\"\"$

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$\"\"$ .

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Angle of force is $\"\"$ .

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$\"\"$

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(b)

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Student exerts $\"\"$ to pull her backpack at an angle of $\"\"$ .

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Work done is $\"\"$ J and $\"\"$ .

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Find the directed distance $\"\"$ .

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Use projection formula for work.

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Projection formula for work: $\"\"$ .

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$\"\"$

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Substitute $\"\"$ , $\"\"$ and $\"\"$ in above expression.

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$\"\"$

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Thus, directed distance is $\"\"$ .

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$\"\"$

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(a) Angle of force is $\"\"$ .

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(b) Directed distance is $\"\"$ .