Engineering Mechanics: Statics & Dynamics (14th Edition)

Published by Pearson
ISBN 10: 0133915425
ISBN 13: 978-0-13391-542-6

Chapter 15 - Kinetics of a Particle: Impulse and Momentum - Section 15.9 - Propulsion with Variable Mass - Problems - Page 310: 139



Work Step by Step

We can determine the required speed as follows: $\int_0^v dv=\int_0^5(\frac{T+qv_{D/e}}{m_{\circ}-qt})$ $\implies v=(\frac{T+qv_{D/e}}{q})\ln(\frac{m_{\circ}}{m_{\circ}-qt})+v_{\circ}$ $\implies v=(\frac{T+2\frac{dW}{dt}\frac{1}{g}v_{D/e}}{2\frac{dW}{dt}})\ln(\frac{W_{\circ}}{W_{\circ}-2qt})+v_{\circ}$ We plug in the known values to obtain: $v=(\frac{15000+2(150)(\frac{1}{32.2})(3000)}{2(150)})ln(\frac{40000}{40000-2(150)})+440$ This simplifies to: $v=580ft/s$
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