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Show that the equation of motion is =-mvert + Feat Specialize to the case of a rocket taking of nstant) gravitational

Show that the equation of motion is =-mvert + Feat Specialize to the case of a rocket taking of nstant) gravitational

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Consider a rocket traveling in a straight line subject to an external force Fext acting along the same line. a) Show that the equation of motion is mú = -mvext + Feat (1) b) Specialize to the case of a rocket taking off vertically (from rest) in a (constant) gravitational field g, so the equation of motion becomes múmvext mg (2) Assume that the rocket ejects mass at a constant rate, m = -k (where k is a positive constant), so that m = mg - kt Solve the equation for v as a function of t.
Transcribed Image Text:Consider a rocket traveling in a straight line subject to an external force Fext acting along the same line. a) Show that the equation of motion is mú = -mvext + Feat (1) b) Specialize to the case of a rocket taking off vertically (from rest) in a (constant) gravitational field g, so the equation of motion becomes múmvext mg (2) Assume that the rocket ejects mass at a constant rate, m = -k (where k is a positive constant), so that m = mg - kt Solve the equation for v as a function of t.
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