$\"\"$

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The minimum velocity required for an object to escape earths gravitational pull is

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$\"\"$ .

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Where $\"\"$ is the velocity of an object, $\"\"$ is the distance from the center of earth, $\"\"$ is gravitational constant and $\"\"$ is the mass of earth.

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Find the relation between $\"\"$ and $\"\"$ .

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$\"\"$

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Apply power rule of integration: $\"\"$ .

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$\"\"$

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The minimum velocity required for an object to escape earths gravitational pull is

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$\"\"$ . $\"\"$

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The initial velocity is $\"\"$ .

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The radius of earth is $\"\"$ .

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The initial velocity required for an object to escape earths gravitational pull:

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

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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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$\"\"$ .