Physics: Principles with Applications (7th Edition)

Published by Pearson
ISBN 10: 0-32162-592-7
ISBN 13: 978-0-32162-592-2

Chapter 12 - Sound - Problems - Page 356: 70

Answer

The plane is a horizontal distance of 16 km away, at a height of 9.5 km.

Work Step by Step

See the figure provided in the textbook for this problem. Find the angle of the shock wave, using equation 12-5. $$\theta = sin^{-1}\frac{v_{sound}}{v_{obj}}= sin^{-1}\frac{v_{sound}}{2.0v_{sound}}= sin^{-1}\frac{1}{2.0}=30^{\circ}$$ Now find the horizontal distance that the plane has traveled when the shock wave reaches the observer. $$tan\theta=\frac{9500m}{L}$$ $$L=\frac{9500m}{tan30^{\circ}}\approx 16\;km$$
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