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Escape veolcity for Earth

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From the conservation theorme for potential plus kinetic energy show that the escape veolcity for Earth, ingnoring the presence of the Moon, is 11.2 km/s.
Classical Mechanics - Escape veolcity for Earth. Classical Mechanics - Escape veolcity for Earth
The escape velocity of a particle on Earth is the minimum velocity requiredat Earth’s surface in order that that particle can escape from Earth’sgravitational field. Neglecting the resistance of the atmosphere, the system isconservative. From the conservation theorme for potential plus kinetic energyshow that the escape veolcity for Earth, ingnoring the presence of the Moon, is11.2 km/s.
(Source: Herbert Goldstein, Classical Mechanics - Chapter 01)
 



Lets plug in the numbers to this simple problem:


This gives v = 1.118 × 104 m/s which is 11.2 km/s.
 
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