Solve the Problem $R$ , When Designing a Road Is $\mathrm { R } = \frac { \mathrm { V } ^ { 2 } } { \mathrm {~g} ( \mathrm { f } + \tan \alpha ) }$

Multiple Choice

Solve the problem.
-A formula used by an engineer to determine the safe radius of a curve, $R$ , when designing a road is: $\mathrm { R } = \frac { \mathrm { V } ^ { 2 } } { \mathrm {~g} ( \mathrm { f } + \tan \alpha ) }$ , 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 $\mathrm { V } = 84 \mathrm { ft }$ per $\mathrm { sec } , \mathrm { f } = 0.1 , \mathrm {~g} = 30$ , and $\alpha = 1.1 ^ { \circ }$ , find $\mathrm { R }$ . Round to the nearest foot.

A) $\mathrm { R } = 1973 \mathrm { ft }$
B) $R = 1977 \mathrm { ft }$
C) $R = 1983 \mathrm { ft }$
D) $\mathrm { R } = 1970 \mathrm { ft }$