WAEC Physics 2020 Theory — Question 5

Model answer

Given: Escape velocity VE, radius of the earth=R. To show that VE=sqrt(2gR). Analysis: When the satellite just escapes the earth's gravitational attraction, the Gravitational potential energy equals the kinetic energy of the satellite, i.e. P.E.=K.E. GmM/R = (1/2)mVE^2. GM/R = (1/2)VE^2. VE^2=2GM/R. But GM=gR^2 (from g=GM/R^2). VE^2=2gR^2/R=2gR. Therefore, VE=sqrt(2gR).