Chapter 5.5, Problem 49E

To determine

At what angle should the curve be banked, if the speed limit on the curve will be 65 miles per hour? (Hint: Change 65 miles per hour to feet per second.)

Answer to Problem 49E

  $\theta \simeq {13.3}^{\circ }$

Explanation of Solution

Given information: Civil Engineering: Highway curves are usually banked or tilted inward so that cars can negotiate the curve more safely. The proper banking angle $\theta$ for a car making a turn of radius r feet at a velocity of v feet per second is given by the equation is $\tan \theta =\frac{v^2}{gr}$ . In this equation, g is the acceleration due to gravity or 32 feet per second squared. An engineer is designing a curve with a radius of 1200 feet.

Calculation:

First, convert miles per hour into feet per second. Simplify replace the word “mile” with 5280 feet and replace hour with 3600 seconds.

  $\begin{array}{l}\frac{65\text{ miles}}{\text{hour}}\to \frac{65\left(5280\text{feet}\right)}{3600\text{ seconds}}=95.3\frac{\text{ft}}{\sec }\\ \tan \theta =\frac{v^2}{gr}=\frac{{95.3}^2}{32\left(1200\right)}\\ \theta ={\tan }^{-1}\left(\frac{{95.3}^2}{32\left(1200\right)}\right)\\ \theta \simeq {13.3}^{\circ }\end{array}$