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: Foundations and Connections

1st Edition

ISBN:9781133939146

Author:Katz, Debora M.

Publisher:Katz, Debora M.

Chapter6: Applications Of Newton’s Laws Of Motion

Section: Chapter Questions

Problem 58PQ: A satellite of mass 16.7 kg in geosynchronous orbit at an altitude of 3.58 104 km above the Earths...

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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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