# Does the escape speed of a body from the earth depend on

Question:

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?

Solution:

(a) No

(b) No

(c) No

(d) Yes

Escape velocity of a body from the Earth is given by the relation:

$v_{\mathrm{esc}}=\sqrt{2 \mathrm{~g} R}$  (i)

g = Acceleration due to gravity

R = Radius of the Earth

It is clear from equation (i) that escape velocity $v_{\text {esc }}$ is independent of the mass of the body and the direction of its projection. However depends on gravitational potential at the point from where the body is launched. Since this potential marginally depends on the height Share the point, escape velocity also marginally depends on these factors.