The weight of a particle varies with altitude such that ? = m(gro2)/r2, where ?0 is the radius of the earth and ? is the distance from the particle to the earth’s center. If the particle is fired vertically with a velocity ?0 rom the earth’s surface, determine its velocity as a function of position ?. What is the smallest velocity ?0 required to escape the earth’s gravitational field, what is the time required to reach the altitude? Show complete Solution and the FBD

acceleration a = W/m = -gro²/r² = dv/dt = dv/dr * dr/dt = dv/dr * v v dv = -gro²/r² drintegrate,v²/2…

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Physics for Scientists and Engineers

10th Edition

ISBN:9781337553278

Author:Raymond A. Serway, John W. Jewett

Publisher:Raymond A. Serway, John W. Jewett

Chapter13: Universal Gravitation

Section: Chapter Questions

Problem 32AP

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The weight of a particle varies with altitude such that ? = m(gr_o²)/r²_, where ?₀ is the radius of the earth and ? is the distance from the particle to the earth’s center. If the particle is fired vertically with a velocity ?₀ rom the earth’s surface, determine its velocity as a function of position ?. What is the smallest velocity ?₀ required to escape the earth’s gravitational field, what is the time required to reach the altitude? Show complete Solution and the FBD

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