The gravitational potential energy acting on a rocket going into space is given

Question

The gravitational potential energy acting on a rocket going into space is given by U = -G mn/r where G is the gravitational constant of the universe equal to 6.67 x 10^-11 m^3 kg^-1 s^-2, m is the mass of the rocket, M is the mass of the earth, and r is the distance from the center of the earth. A rocket can escape earth's gravity if it can reach a potential energy of U = 0. Using this information, what velocity must a rocket have to escape earth's gravity if it starts on the surface of the earth?

Explanation / Answer

                 potential energy     U = -G Mm / r   According to law of conservation of energy                 initial kinetic energy   + inital potentail energy =                                                                                      potential eenrgy   + final kinetic energy              (1/2)mv2   - GMm /r     =   0 + 0                                                 (1/2)mv2      = GMm /r    ==>    v   = sqrt ( 2GM/r )                                  GM/r2   = g   = accelaration due to gravity = 9.8 m/s^2               escape velocity   v   =   sqrt ( 2gr )                Here   r = radius of the earth = 6.4 *106 m                plug all values we get v   = 11.2 km /s                                      

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