Solve the Problem $\mathrm { R } = \frac { \mathrm { V } ^ { 2 } } { g ( \mathrm { f } + \tan \alpha ) }$

question 213

Multiple Choice

Solve the problem.
-A formula used by an engineer to determine the safe radius of a curve, R, when designing a particular road is: $\mathrm { R } = \frac { \mathrm { V } ^ { 2 } } { g ( \mathrm { f } + \tan \alpha ) }$ , where $\alpha$ is the superelevation of the road and $\mathrm { V }$ is the velocity (in feet per second) for which the curve is designed. If $\alpha = 2.1 ^ { \circ } , \mathrm { f } = 0.1 , \mathrm {~g} = 30$ , and $\mathrm { R } = 1195.11 \mathrm { ft }$ , find V. Round to the nearest foot per second.

• A) \(V = 68 \mathrm { ft }\) per sec
• B) \(V = 73 \mathrm { ft }\) per sec
• C) \(\mathrm { V } = 70 \mathrm { ft }\) per sec
• D) \(V = 66 \mathrm { ft }\) per sec

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Definitions:

Sum Of Squares

A statistical measure that quantifies the dispersion or variation within a data set, typically used in variance and regression analysis.

Regression SSR

The sum of squares due to regression, indicating the explained variance by the regression model in the data.

Error SSE

The sum of squared errors in statistical analysis, indicating the discrepancy between observed and predicted values.

Allman Brothers

A Southern rock band formed in 1969, known for their significant influence on the genre with hits like "Ramblin' Man" and "Midnight Rider."