Does the escape speed of a body from the earth depend on (a) the mass of the body, (b) the location from where it is projected, (c) the direction of projection, (d) the height of the location from where the body is launched?

Escape speed is the minimum speed a body must acquire in order to move out of earth’s gravitational field or escape from earth’s influence. This happens when total energy body becomes zero or positive and is in the unbound state.

(a)No, Escape speed does not depend upon the mass of the body as escape speed is given by the relation

Here, VS is escape velocity of a body at a distance of R from the centre of earth G is universal Gravitational Constant, Me is the mass of earth

So as we can see the relation of escape velocity is independent of the mass of body itself.

(b) No, Escape speed does not depend upon location from where it is projected assuming the condition that earth is a perfect sphere and radius of earth’s surface is almost same everywhere, because then according to relation of escape velocity, the distance from centre of earth R will be a constant value irrespective of latitude and longitude hence the escape speed is invariant of location.

(c) No, Escape speed does not depend upon the direction of projection as we take any direction value of gravitational Constant G, the mass of earth Me and Radius at the surface of earth R will be constant so escape speed will be constant. Though if we take earth’s spin into account as well then the value will depend on direction though we are neglecting it here.

(d) Yes, Escape speed depends on the height of the location from where the body is launched as we can see in the relation escape velocity varies inversely to the square root of the distance from the centre of the earth

Where Vs is escaped speed and R is the distance from the centre of the earth

Now as the height of body from the surface of the earth increases its distance from the centre of earth increases and Escape velocity decreases.