Solve the Problem $R$ , When Designing a Particular 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 particular 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 $\alpha = 2.1 ^ { \circ } , \mathrm { f } = 0.1 , \mathrm {~g} = 30$ , and $\mathrm { R } = 1229.5 \mathrm { ft }$ , find V. Round to the nearest foot per second.

A) $\mathrm { V } = 74 \mathrm { ft }$ per sec
B) $V = 69 \mathrm { ft }$ per sec
C) $V = 71 \mathrm { ft }$ per sec
D) $V = 67 \mathrm { ft }$ per sec