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I ended up finding a solution for this question, but I am not understanding the last part of it. How did they simply the part outlined in red to ft/ft? I may be overthinking this, but I can't seem to figure it out.

I ended up finding a solution for this question, but I am not understanding the last part of it. How did they simply the part outlined in red to ft/ft? I may be overthinking this, but I can't seem to figure it out.

College Physics
College Physics
11th Edition
ISBN:9781305952300
Author:Raymond A. Serway, Chris Vuille
Publisher:Raymond A. Serway, Chris Vuille
Chapter1: Units, Trigonometry. And Vectors
Section: Chapter Questions
Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...
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I ended up finding a solution for this question, but I am not understanding the last part of it. How did they simply the part outlined in red to ft/ft? I may be overthinking this, but I can't seem to figure it out.

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 S = 2g(f + 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/s2 f = coefficient of friction between tires and roadways G = grade of road T = driver reaction time (s) 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. v2 Starting with the equation S + TV, the units of S are ft, the units of V2 are --?-- , the units of g are ft/s2, %3D 2g(f + G) and the units of the product TV are --?-- Rearranging the equation above to solve for f ± G, we obtain the following. (Use any variable or symbol stated above as necessary. Do not substitute numerical values; use variables only.) f+ G = ft2/s? Then, the units of f+ G are = --?-- --?--
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 v2 S = 2g(f + 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/s2 f = coefficient of friction between tires and roadways G = grade of road T = driver reaction time (s) 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. v2 Starting with the equation S + TV, the units of S are ft, the units of V2 are --?-- , the units of g are ft/s2, %3D 2g(f + G) and the units of the product TV are --?-- Rearranging the equation above to solve for f ± G, we obtain the following. (Use any variable or symbol stated above as necessary. Do not substitute numerical values; use variables only.) f+ G = ft2/s? Then, the units of f+ G are = --?-- --?--
Formula used: The model proposed by the American Association of State Highway Officials (AASHO) is, v? + TV (1) 2g(f±G) S = Here, S is the stopping sight distance, V is the initial speed, f is the coefficient of friction between tires and roadways, G is grade of road, g is the acceleration due to gravity, and T is the driver reaction time. Calculation: Rearrange the equation (1) as follows, y2 2g(f±G) (2) S- TV = V2 (f ± G) = 2g(S–TV) Substitute the unit ft for S, " for V, s for T and " for g in equation (2) to find f and G. (#)' 2(골) (1-10)()) (2) 2(플)(R-10) (f± G) = The ratio of " is results to G, f are unitless. Therefore, the grad of road (G) and coefficient of friction (f) are unitless. Conclusion: Hence, the grad of road (G) and coefficient of friction (f) are unitless.
Transcribed Image Text:Formula used: The model proposed by the American Association of State Highway Officials (AASHO) is, v? + TV (1) 2g(f±G) S = Here, S is the stopping sight distance, V is the initial speed, f is the coefficient of friction between tires and roadways, G is grade of road, g is the acceleration due to gravity, and T is the driver reaction time. Calculation: Rearrange the equation (1) as follows, y2 2g(f±G) (2) S- TV = V2 (f ± G) = 2g(S–TV) Substitute the unit ft for S, " for V, s for T and " for g in equation (2) to find f and G. (#)' 2(골) (1-10)()) (2) 2(플)(R-10) (f± G) = The ratio of " is results to G, f are unitless. Therefore, the grad of road (G) and coefficient of friction (f) are unitless. Conclusion: Hence, the grad of road (G) and coefficient of friction (f) are unitless.
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