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Physics / Sears and Zemansky's University Physics with Modern Physics 13 / Chapter 2 / Problem 24E

Sears and Zemansky's University Physics with Modern Physics | 13th Edition | ISBN: 9780321696861 | Authors: Hugh D. Young; Roger A. Freedman; A. Lewis Ford

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Solved: BIO A pilot who accelerates at more than 4 g

Chapter 2, Problem 24E

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QUESTION:

Problem 24E

BIO A pilot who accelerates at more than 4 g begins to “gray out” but doesn’t completely lose consciousness. (a) Assuming constant acceleration, what is the shortest time that a jet pilot starting from rest can take to reach Mach 4 (four times the speed of sound) without graying out? (b) How far would the plane travel during this period of acceleration? (Use 331 m/s for the speed of sound in cold air.)

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QUESTION:

Problem 24E

BIO A pilot who accelerates at more than 4 g begins to “gray out” but doesn’t completely lose consciousness. (a) Assuming constant acceleration, what is the shortest time that a jet pilot starting from rest can take to reach Mach 4 (four times the speed of sound) without graying out? (b) How far would the plane travel during this period of acceleration? (Use 331 m/s for the speed of sound in cold air.)

ANSWER:

Solution 24E

Step 1

If $a$ is the acceleration $u$ is the initial velocity and $v$ is the final velocity then the time required to increase the velocity is given by

So the pilot have to increase the speed from zero to Mach 4 with acceleration $4g$ . So we have

$u=0\ m/s$

$v=4\times{}(331\ m/s)=1324\ m/s$

$a=4g=4(9.8\ m/{s}^{2})=39.2\ m/{s}^{2}$

So the required time is

So the shortest time at which the jet pilot starting from rest can reach Mach 4 is 33.8 s.

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