11th Edition

ISBN: 9781337652469

Author: ZILL

Publisher: CENGAGE L

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Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differentia…

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Textbook Question

Chapter 1.3, Problem 22E

In Problem 21, the mass m(t) is the sum of three different masses: m(t) = m_p + m_v + m_f(t), where m_p is the constant mass of the payload, m_v is the constant mass of the vehicle, and m_f(t) is the variable amount of fuel.

(a) Show that the rate at which the total mass m(t) of the rocket changes is the same as the rate at which the mass m_f(t) of the fuel changes.
(b) If the rocket consumes its fuel at a constant rate λ, find m(t). Then rewrite the differential equation in Problem 21 in terms of λ and the initial total mass m(0) = m₀.
(c) Under the assumption in part (b), show that the burnout time t_b > 0 of the rocket, or the time at which all the fuel is consumed, is t_b = m_f(0)/λ, where m_f(0) is the initial mass of the fuel.

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Chapter 1.3, Problem 21E

Chapter 1.3, Problem 23E

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Solution Summary: The author explains that the rate at which the total mass of the rocket changes is the same as that of its fuel.

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