$\"\"$

\

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

\

$\"\"$ .

\

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

\

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

\

$\"\"$

\

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

\

$\"\"$

\

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

\

$\"\"$ .

\

$\"\"$

\

The initial velocity is $\"\"$ .

\

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

\

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

\

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

\

$\"\"$

\

$\"\"$ .

\

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

\

$\"\"$

\

$\"\"$ .

\

$\"\"$

\

$\"\"$ .