Solve the Problem $\mathrm { V }$ (In Feet Per Second), the Safe Radius

question 173

Multiple Choice

Solve the problem.
-If an automobile is traveling at velocity $\mathrm { V }$ (in feet per second) , the safe radius $\mathrm { R }$ for a curve with superelevation $\alpha$ is given by the formula $\mathrm { R } = \frac { \mathrm { V } ^ { 2 } } { \mathrm {~g} ( \mathrm { f } + \tan \alpha ) }$ , where $\mathrm { f }$ and $g$ are constants. A road is being constructed for automobiles traveling at 47 miles per hour. If $\alpha = 4 ^ { \circ } , g = 31.5$ , and $f = 0.16$ , calculate $R$ . Round to the nearest foot. (Hint: 1 mile $= 5280$ feet)

• A) \(R = 656 \mathrm { ft }\)
• B) \(R = 1106 \mathrm { ft }\)
• C) \(R = 640 \mathrm { ft }\)
• D) \(\mathrm { R } = 676 \mathrm { ft }\)

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Definitions:

Incentive

A thing that motivates or encourages someone to do something, often seen as a reward or punishment scheme in behavioral psychology.

Drive

An inner motivation or urge that propels an individual to act or achieve certain goals.

Optimal Stimulation

A psychological theory proposing that individuals seek an optimal level of arousal, with too little leading to boredom and too much resulting in stress.

Arousal Theory

The theory that optimal performance and psychological arousal are related in a way that differs as a function of the individual and the task.