Gilbert Strang, Calculus, 3rd edition (Wellesley-Cambridge Press; MIT OpenCourseWare RES.18-001) §8.6 Force, Work, and Energy, #12 · Calculus · Applications of integrals

The kinetic energy … of a rocket is converted into potential energy…

The kinetic energy $\frac{1}{2} m v^{2}$ of a rocket is converted into potential energy $- GM m / x$ . Starting from the Earth's radius $x = R$ , what $x$ does the rocket reach? If it reaches $x = \infty$ show that $v = 2 GM / R$ . This escape velocity is 25,000 miles per hour.

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Gilbert Strang, Calculus, 3rd edition (Wellesley-Cambridge Press; MIT OpenCourseWare RES.18-001) · §8.6 Force, Work, and Energy, #12

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