$\"\"$

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The combined weight of Malcolm $\"\"$ s sister and the wagon is the force exerted due to gravity, $\"\"$ .

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To find the force $\"\"$ required to keep her from sliding down the slope, project $\"\"$ onto a unit vector $\"\"$ in the direction of the side of the hill.

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$\"\"$

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Find a unit vector $\"\"$ in the direction of the side of the hill.

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$\"\"$

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$\"\"$

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$\"\"$

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Find $\"\"$ , the projection of $\"\"$ onto the unit vector $\"\"$ , $\"\"$ .

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Projection of $\"\"$ onto $\"\"$ : $\"\"$ .

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$\"\"$

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$\"\"$ .

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Since $\"\"$ points down the hill, the force required is $\"\"$ .

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Since $\"\"$ is a unit vector, $\"\"$ represents the magnitude of the force required to keep Malcolm $\"\"$ s sister from sliding down the hill.

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$\"\"$

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The magnitude of the force required to keep Malcolm $\"\"$ s sister from sliding down the hill is $\"\"$ .