What is the escape velocity of a body on the surface of the earth of radius R if the gravitational constant is G and the mass of the earth is M? (Neglect energy losses to the surroundings)
Set initial total energy to zero:
\(\frac{1}{2}mv^2 - \frac{GMm}{R} = 0\)
\(\frac{1}{2}mv^2 = \frac{GMm}{R}\)
\(v^2 = \frac{2GM}{R}\)
\(v = \sqrt{\frac{2GM}{R}}\)
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