Book edition 10th Edition

Author(s) David Halliday

Pages 1328 pages

ISBN 9781118230718

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Short Answer

The terminal speed of a sky diver is $^{160 km / h}$ in the spread-eagle position and $^{310 km / h}$ in the nosedive position. Assuming that the diver’s drag coefficient C does not change from one position to the other, find the ratio of the effective cross-sectional area A in the slower position to that in the faster position.

The ratio of the effective cross-sectional area A in the slower position to that in the faster position is $^{3.75}$

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Step by Step Solution

TABLE OF CONTENTS :

TABLE OF CONTENTS

Step 1: Given

$a = \frac{2 m g}{C p {v^{2}}_{t}}$

which illustrates the inverse proportionality between the area and the speed-squared

thus

$A_{s l o w} = 310 km / h A_{f a s t =} 160 km / h$

Step 2: Determining the concept

This problem is based on the drag force which is a type of friction. This is the force acting opposite to the relative motion of an object moving with respect to the surrounding medium. Using the concept of the drag force and terminal speed the ratio of the effective cross-sectional area A in the slower position to that in the faster position.

Formula:

The terminal speed is given by

$v_{t} = \sqrt{\frac{2 F_{g}}{C p A}}$

Where C is the drag coefficient, $^{p}$ is the fluid density, A is the effective cross-sectional area, and $^{F_{g}}$ is the gravitational force.

solve for the area

$A = \frac{2 m g}{C p {v^{2}}_{t}}$

which illustrates the inverse proportionality between the area and the speed-squared

Step 3: Determining the ratio of the effective cross-sectional area A in the slower position to that in the faster position

When a ratio of areas has been setup of the slower case to the faster case,

$\frac{A_{s l o w}}{A_{f a s t}} = {(\frac{110 km / h}{160 km / h})}^{2} = 3.75$

Hence, the ratio of the effective cross-sectional area A in the slower position to that in the faster position is $^{3.75}$

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Fundamentals Of Physics

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Short Answer

Step by Step Solution

Step 1: Given

Step 2: Determining the concept

Step 3: Determining the ratio of the effective cross-sectional area A in the slower position to that in the faster position

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