Question

Suppose a rocket is fired from the earth's surface of radius r, so that it just escapes from the gravitational influence of the earth with velocity v, then v is given by

Answer 1

By the definition, the escape velocity is given by:

$$KE=PE,$$ $$\dfrac{1}{2}mv^2=GM_Emr,$$ $$v_{esc}=\sqrt{\dfrac{2GM_E}{r}}$$