$\"\"$

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Let $\"\"$ represent the point where rope and pole are to be connected and $\"\"$ be the point where ball is being served.

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Vector coordinates of points $\"\"$ and $\"\"$ .

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$\"\"$ vector represents the vector from the pole to the ball.

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The component form of $\"\"$ and $\"\"$ is $\"\"$ .

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Let the points are $\"\"$ and $\"\"$ .

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The component form $\"\"$ .

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$\"\"$

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$\"\"$

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Magnitude of $\"\"$ is $\"\"$ .

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$\"\"$

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$\"\"$

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Magnitude of the vector represents the length of the rope is $\"\"$ feet long.

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$\"\"$

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Magnitude of the vector represents the length of the rope is $\"\"$ feet long.