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

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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:

\[\frac{\text{ft}^2/\text{s}^2}{\_\_\_\_\} = \_\_\_\_\ .\]
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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