ESCAPE VELOCITY EXPLANATION - HOW DO WE FIND THE ESCAPE VELOCITY OF EARTH?

 If we want to escape from Earth, we just need to travel at a velocity of 11.2 Kms^-1   

^{Because this is the escape velocity of Earth. Otherwise, we come back to Earth, because of gravity. Rockets must travel this velocity from the initial in the earth's surface.} 

^{How to measure?}

Consider a Rocket that wants to go to space. The mass of the Rocket M. Initial velocity of Rocket v.

 Any object that travels vertically(like a rocket) must have kinetic energy.

          E_i = 1/2 mv²

^{But the object moves earth vertically, it has gravitational potential so that,}

           E_i = 1/2 mv²   -  GMM_E/R_{E .........(1)}

When the rocket reaches a height far away from Earth, gravitational potential energy becomes zero and kinetic energy is also zero. 
                          

         E_{f   = 0   ............................(2)} 

          E_i  = E_{f    ................................(3)}

       _{½ mv} ²   – GMM_E/R_E  =  0 ..............(4)

       ½ mv ²   =  GMM_E/R_{E   ......................(5)}

        V²_e        =  2g_ER_{E         ........................(6)}

         V_e        =   11.2 Kms^{-1 ...............................(7)}   

^{This is the required velocity to escape a rocket from Earth.}