Arrive at the expression for escape speed of the body from the surface of earth.

Explanation

For a satelite to escape into infinite orbit,
`Delta PE=PE_(oo)-PE_(r ) because PE_(oo)=0" "Delta PE=-(-(GMm)/(R+h))`
But `K.E=P.E.`
`(1)/(2) cancel(m)V_e^2=(GM cancel(m))/(R+h)` i.e., `v_e=sqrt((2(GM))/((R+h)))` for `h=0 v_e=sqrt((2GM)/(R ))=sqrt(2gR)`
It is assumed that at infinite distance `PE =0,v_i=0.`
It is a free fall of an object from the point of infinity to a point on the surface in the absence of any frictional forces.