$\"\"$

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The function is $\"\"$ .

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The fleeing object leaves the origin and moves the up $\"\"$ -axis.

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Substitute $\"\"$ .

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$\"\"$ .

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The fleeing object is travelled $\"\"$ units when it is caught.

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$\"\"$

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Definition Of Arc Length :

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Let the function given by $\"\"$ represent a smooth curve on the interval $\"\"$ .

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The arc length of $\"\"$ between $\"\"$ and $\"\"$ is $\"\"$ .

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Where $\"\"$ is $\"\"$ .

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The function is $\"\"$ .

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Apply derivative on each side with respect to $\"\"$ .

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$\"\"$

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$\"\"$

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$\"\"$

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$\"\"$ .

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$\"\"$

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Substitute $\"\"$ in $\"\"$ .

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$\"\"$

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$\"\"$ .

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$\"\"$

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$\"\"$

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$\"\"$

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$\"\"$

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$\"\"$ .

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$\"\"$

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The distance travelled by pursuer is $\"\"$ .

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The distance travelled by fleeing object is $\"\"$ .

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Hence, $\"\"$ .

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Therefore, the pursuer has travelled twice the distance travelled by the fleeing object.

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$\"\"$

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The pursuer has travelled twice the distance travelled by the fleeing object.