Trigonometry (11th Edition) Clone

Published by Pearson
ISBN 10: 978-0-13-421743-7
ISBN 13: 978-0-13421-743-7

Chapter 2 - Acute Angles and Right Triangles - Section 2.3 Finding Trigonometric Function Values Using a Calculator - 2.3 Exercises - Page 68: 78

Answer

$R=791 ft$

Work Step by Step

We are using the formula $R=\frac{V^{2}}{g(f+\tan\theta)}$ where R is the safe radius of the curve, V is the velocity in feet per second, $\theta$ is the superelevation and $f$ and $g$ are constants to calculate the radius of the curve. In this case taking the values from Exercise 77 with the new velocity $V=70mph$, $\theta=3^{\circ}$ $g=32.2$ $f=0.14$ Converting the miles per hour to feet per second, with the hint from Exercise 77: $45mph=66ft/s$ $V=70mph*\frac{66ft/s}{45mph}=102.7ft/s$ Substituting in the formula, $R=\frac{102.7^{2}}{32.2(0.14+\tan(3^{\circ}))}$ $R=1702ft$ (rounded to the nearest feet)
Update this answer!

You can help us out by revising, improving and updating this answer.

Update this answer

After you claim an answer you’ll have 24 hours to send in a draft. An editor will review the submission and either publish your submission or provide feedback.