(i) Define escape velocity

(i) Define escape velocity.
(ii) Derive expression for the escape velocity of an object from the surface of planet.
(iii) Does it depend on location from where it is projected ?

(i) Escape velocity on earth (or any other planet) is defined as the minimum velocity with which the body has to be projected vertically upwards from the surface of earth (or any other planet) so that it just crosses the gravitational field of earth (or of that planet) and never returns on its own.
(ii)Let earth be a perfect sphere o| mass M, radius R with centre at O. Let a body of mass m to be projected from a point A on the surface of earth (planet). Join OA and produce it further. Take two points P and Q at a distance x and (x + dx) from the centre O of the earth.

The value of escape velocity depends upon the mass and radius of the planet of the surface from which the body is to be projected. Clearly, the values of escape velocity of a body will be different for different planets.