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

Explanation

For a satellite to escape into infinite orbit,
`DeltaPE=PE_(oo)-PE_(r):'PE_(oo)=0" " DeltaPE=-(-(GMm)/(R+H))`
But K.e = P.e
`1/2cancelmV_(e)^(2)=(GMcancelm)/(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.