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64. Escape Velocity The minimum velocity required for an object to escape Earth's gravitational pull is obtained from the solution of the equation [v dv = - GMS 1/2 dy where v is the velocity of the object projected from Earth, y is the distance from the center of Earth, G is the gravitational constant, and M is the mass of Earth. Show that v and y are related by the equation v² = √² + 2GM (1 - 1) y R where vo is the initial velocity of the object and R is the radius of Earth.

64. Escape Velocity The minimum velocity required for an object to escape Earth's gravitational pull is obtained from the solution of the equation [v dv = - GMS 1/2 dy where v is the velocity of the object projected from Earth, y is the distance from the center of Earth, G is the gravitational constant, and M is the mass of Earth. Show that v and y are related by the equation v² = √² + 2GM (1 - 1) y R where vo is the initial velocity of the object and R is the radius of Earth.

College Physics
College Physics
11th Edition
ISBN:9781305952300
Author:Raymond A. Serway, Chris Vuille
Publisher:Raymond A. Serway, Chris Vuille
Chapter1: Units, Trigonometry. And Vectors
Section: Chapter Questions
Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...
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64. Escape Velocity The minimum velocity required for an object to escape Earth's gravitational pull is obtained from the solution of the equation [v dv = - GMS ²/3 d where v is the velocity of the object projected from Earth, y is the distance from the center of Earth, G is the gravitational constant, and M is the mass of Earth. Show that v and y are related by the equation y² = √² + 2GM (1 - 1/2) R where v is the initial velocity of the object and R is the radius of Earth.
Transcribed Image Text:64. Escape Velocity The minimum velocity required for an object to escape Earth's gravitational pull is obtained from the solution of the equation [v dv = - GMS ²/3 d where v is the velocity of the object projected from Earth, y is the distance from the center of Earth, G is the gravitational constant, and M is the mass of Earth. Show that v and y are related by the equation y² = √² + 2GM (1 - 1/2) R where v is the initial velocity of the object and R is the radius of Earth.
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