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

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 50 miles per hour. If $\alpha = 4 ^ { \circ } , \mathrm { g } = 32.4$ , and $\mathrm { f } = 0.16$ , calculate R. Round to the nearest foot. (Hint: 1 mile $= 5280$ feet)

A) $R = 1172 \mathrm { ft }$
B) $R = 706 \mathrm { ft }$
C) $R = 722 \mathrm { ft }$
D) $\mathrm { R } = 742 \mathrm { ft }$