Physics for Scientists and Engineers: A Strategic Approach with Modern Physics (3rd Edition)

Published by Pearson
ISBN 10: 0321740904
ISBN 13: 978-0-32174-090-8

Chapter 9 - Impulse and Momentum - Exercises and Problems - Page 242: 39

Answer

$-31.5\;\rm m/s$

Work Step by Step

Since the drag force is negligible during the small time interval of expelling the water, the system [Squids+ejected water] is isolated. So that the momentum is conserved and hence, $$p_{ix}=p_{fx}$$ The Squids plus ejected water are initially one unit, so $$(m_w+m_s)v_{ix}=m_wv_{fx,w}+m_sv_{fx,s}$$ where $w$ refers to the ejected water, and $s$ refers to the squids. Solving for $v_{fx,w}$; $$v_{fx,w} =\dfrac{(m_w+m_s)v_{ix} -m_sv_{fx,s} }{m_w}$$ Plugging the known; $$v_{fx,w} =\dfrac{[(0.1+1.5)\times 0.40 ] -(1.5\times2.5) }{0.1}$$ $$v_{fx,w} =\bf -31.1\;\rm m/s$$ Thus, the speed of the ejected water relative to the squids is given by $$v'_{fx,w} =v_{fx,w} -v_{ix,s} = -31.1-0.40 =\color{red}{\bf -31.5}\;\rm m/s $$
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