StudySmarter AI is coming soon!

- :00Days
- :00Hours
- :00Mins
- 00Seconds

A new era for learning is coming soonSign up for free

Suggested languages for you:

Americas

Europe

Q36P

Expert-verifiedFound in: Page 143

Book edition
10th Edition

Author(s)
David Halliday

Pages
1328 pages

ISBN
9781118230718

**The terminal speed of a sky diver is ${}^{\mathbf{160}\mathbf{}\mathbf{km}\mathbf{/}\mathbf{h}}$ in the spread-eagle position and ${}^{\mathbf{310}\mathbf{}\mathbf{km}\mathbf{/}\mathbf{h}}$ 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 ${}^{3.75}$

$a=\frac{2mg}{Cp{{v}^{2}}_{t}}$

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

thus

${A}_{slow}=310\mathrm{km}/\mathrm{h}\phantom{\rule{0ex}{0ex}}{A}_{fast=}160\mathrm{km}/\mathrm{h}$

**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

${v}_{t}=\sqrt{\frac{2{F}_{g}}{CpA}}$

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

$A=\frac{2mg}{Cp{{v}^{2}}_{t}}$

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

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

$\frac{{A}_{slow}}{{A}_{fast}}={\left(\frac{110\mathrm{km}/\mathrm{h}}{160\mathrm{km}/\mathrm{h}}\right)}^{2}\phantom{\rule{0ex}{0ex}}=3.75$

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

94% of StudySmarter users get better grades.

Sign up for free