University Physics with Modern Physics (14th Edition)

Published by Pearson
ISBN 10: 0321973615
ISBN 13: 978-0-32197-361-0

Chapter 2 - Motion Along a Straight Line - Problems - Exercises - Page 60: 2.24

Answer

(a) The shortest time to reach Mach 4 without graying out is 33.8 seconds. (b) The plane would travel 22.4 km.

Work Step by Step

(a) Let's assume the pilot is accelerating at 4g. $t = \frac{v-v_0}{a} = \frac{4\times 331~m/s - 0}{4g}$ $t = \frac{331~m/s}{9.80~m/s^2} = 33.8~s$ The shortest time to reach Mach 4 without graying out is 33.8 seconds. (b) $x = \frac{1}{2}at^2$ $x = \frac{1}{2}(4)(9.80~m/s^2)(33.8~s)^2$ $x = 22,400~m = 22.4~km$ The plane would travel 22.4 km.
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