Question

A body is released at a distance r(r>R) from the centre of the earth. What is the velocity of the body when it strikes the surface of the earth?

Answer 1

We will take the potential energy as the kinetic energy  
 
Potential energy is zero at infinity, it is always negative, more negative more faster.  
r = 0  
 
Potential energy at r U= -m GMe/r  
at Re this is-m GMe/Re  
the U will go from r to Re 
UatRe -Uat r =-m GMe/Re-(-m GMe/r)  
so there will be no U when it falls=  m GMe(1/Re - 1/r)  
so  
(1/2)m v^2 = G m Me(1/Re - 1/r)  
or  
v^2 = 2 G Me (r -Re)/(r Re)