pls derive the equation for escape velocity?!!??!!!!?

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this derivation is based on energy conservation ....

when satellite is at earth surface then

total energy = PE + KE

PE = -GMm/R     , (KE)_i = ?                       (M is mass of earth )

TE = (KE)_i - GMm/R           .....1                  (R is radius of earth)

when satellite escapes from earths gravitational field then it reaches to infinity ...

total energy finally = TE = KE + PE

PE = GMm/r          ( r is infinity )

PE = 0 , (KE)_f = ?

TE = (KE)_f  +  0 = (KE)_f   .............2

since energy is conserved so eq 1 equals eq 2

-GMm/R + (KE)_i = (KE)_f

   (KE)_i  = GMm/R +  (KE)_f        .................3

from this eq we can see that if (KE)_f is 0 then (KE) intial is minimum 

value of energy should be given to satellite so that it escapes out...

now , (KE)_i = mv²/2 ,  (KE)_f = 0 , putting these values in eq 3 we get

v = (2GM/R)^1/2

this is the required result...