Explanation Given: The minimum velocity required to escape the earth’s gravitation pull is obtained from the solution of the equation, ∫ v d v = − G M ∫ 1 y 2 d y Where, v is the velocity of the object projectile from the earth, y is the distance from the center of the earth, G is the gravitational constant, and M is the mass of the Earth. The equation, v 2 = v 0 2 + 2 G M ( 1 y − 1 R ) Where, v 0 is the initial velocity of the object and R is the radius of the Earth. Formula used: Integration, ∫ x n d x = x n + 1 n + 1 + C . Proof: The minimum velocity required to escape the earth’s gravitation pull is obtained from the solution of the equation, ∫ v d v = − G M ∫ 1 y 2 d y Integrate the above equation, v 2 2 = − G M ( y − 1 − 1 ) + C = G M ( 1 y ) + C The initial velocity of an object is v 0 at the radius R

11th Edition

ISBN: 9781337275347

Author: Ron Larson, Bruce H. Edwards

Publisher: Cengage Learning

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Chapter 4.1, Problem 64E

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To prove: The v and y are related by the equation, v2=v02+2GM(1y−1R).

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Chapter 4.1, Problem 63E

Chapter 4.1, Problem 65E

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To prove: The v and y are related by the equation, v 2 = v 0 2 + 2 G M ( 1 y − 1 R ) .

Solution Summary: The author explains that the minimum velocity required to escape the earth's gravitation pull is obtained from the solution of the equation.

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To prove: The v and y are related by the equation, v2=v02+2GM(1y−1R).

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