In an experiment performed at the bottom of a very deep vertical mine shaft, a ball is tossed vertically in the air with a known initial velocity of 10.0 m/s, and the maximum height the ball reaches (measured from its launch point) is determined to be 5.113 m. Knowing the radius of the Earth, RE = 6370 km, and the gravitational acceleration at the surface of the Earth, g(0) = 9.81 m/s2, calculate the depth of the shaft.
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