A model known as stopping sight distance is used by civil engineers to design roadways. This simple model estimates the distance a driver needs in order to stop his car while traveling at a certain speed after detecting a hazard. The model proposed by the American Association of State Highway Officials (AASHO) is given by v2 + TV, 2g(f + G) where we have the following. S = stopping sight distance (ft) V = initial speed (ft/s) g = acceleration due to gravity, 32.2 ft/s2 f = coefficient of friction between tires and roadways
A model known as stopping sight distance is used by civil engineers to design roadways. This simple model estimates the distance a driver needs in order to stop his car while traveling at a certain speed after detecting a hazard. The model proposed by the American Association of State Highway Officials (AASHO) is given by v2 + TV, 2g(f + G) where we have the following. S = stopping sight distance (ft) V = initial speed (ft/s) g = acceleration due to gravity, 32.2 ft/s2 f = coefficient of friction between tires and roadways
Elements Of Electromagnetics
7th Edition
ISBN:9780190698614
Author:Sadiku, Matthew N. O.
Publisher:Sadiku, Matthew N. O.
ChapterMA: Math Assessment
Section: Chapter Questions
Problem 1.1MA
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![A model known as **stopping sight distance** is used by civil engineers to design roadways. This simple model estimates the distance a driver needs in order to stop his car while traveling at a certain speed after detecting a hazard. The model proposed by the American Association of State Highway Officials (AASHO) is given by:
\[ S = \frac{V^2}{2g(f \pm G)} + TV, \]
where we have the following:
- \( S = \) stopping sight distance (ft)
- \( V = \) initial speed (ft/s)
- \( g = \) acceleration due to gravity, 32.2 ft/s\(^2\)
- \( f = \) coefficient of friction between tires and roadways
- \( G = \) grade of road
- \( T = \) driver reaction time (s)
---
**Problem:**
What are the appropriate units for \( f \) and \( G \) if the preceding equation is to be homogeneous in units? Show all steps of your work.
- Starting with the equation \( S = \frac{V^2}{2g(f \pm G)} + TV \), the units of \( S \) are ft, the units of \( V^2 \) are \(\_\_\_\_\), the units of \( g \) are ft/s\(^2\), and the units of the product \( TV \) are \(\_\_\_\_\). Rearranging the equation above to solve for \( f \pm G \), we obtain the following. (Use any variable or symbol stated above as necessary. Do not substitute numerical values; use variables only.)
\[ f \pm G = \]
- Then, the units of \( f \pm G \) are:
\[\frac{\text{ft}^2/\text{s}^2}{\_\_\_\_\} = \_\_\_\_\ .\]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F2ac80b65-e9ab-4289-a518-468086809e82%2F78ba3e30-b785-4078-b2f2-1167540d9738%2Fi6xjwoo_processed.jpeg&w=3840&q=75)
Transcribed Image Text:A model known as **stopping sight distance** is used by civil engineers to design roadways. This simple model estimates the distance a driver needs in order to stop his car while traveling at a certain speed after detecting a hazard. The model proposed by the American Association of State Highway Officials (AASHO) is given by:
\[ S = \frac{V^2}{2g(f \pm G)} + TV, \]
where we have the following:
- \( S = \) stopping sight distance (ft)
- \( V = \) initial speed (ft/s)
- \( g = \) acceleration due to gravity, 32.2 ft/s\(^2\)
- \( f = \) coefficient of friction between tires and roadways
- \( G = \) grade of road
- \( T = \) driver reaction time (s)
---
**Problem:**
What are the appropriate units for \( f \) and \( G \) if the preceding equation is to be homogeneous in units? Show all steps of your work.
- Starting with the equation \( S = \frac{V^2}{2g(f \pm G)} + TV \), the units of \( S \) are ft, the units of \( V^2 \) are \(\_\_\_\_\), the units of \( g \) are ft/s\(^2\), and the units of the product \( TV \) are \(\_\_\_\_\). Rearranging the equation above to solve for \( f \pm G \), we obtain the following. (Use any variable or symbol stated above as necessary. Do not substitute numerical values; use variables only.)
\[ f \pm G = \]
- Then, the units of \( f \pm G \) are:
\[\frac{\text{ft}^2/\text{s}^2}{\_\_\_\_\} = \_\_\_\_\ .\]
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