Chapter 4.9, Problem 5ES

Suppose a body of mass m is traveling vertically upward starting at the surface of the earth. If all resistance except gravity is neglected, the escape velocity υ is given by

${\upsilon }^2=2gR{\displaystyle {\int }_1^{\infty }{z}^{-2}dz,}$     where $z=\frac{x}{R}$,

R = 3960 miles is the radius of the earth, and g = 0.00609 mi/s² is the force of gravity at the earth’s surface. Approximate the escape velocity υ.