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) $\mathrm { R } = 1970 \mathrm { ft }$

Question

Quizplus · Accepted Answer

First, convert $\alpha = 1.1^\circ$ to radians because the tangent function in most calculators uses radians. $1.1^\circ = \frac{1.1 \pi}{180}$ radians. Then, substitute the given values into the formula: $R = \frac{84^2}{30(0.1 + \tan(\frac{1.1\pi}{180}))}$. Calculating this gives $R \approx 1973$ feet when rounded to the nearest foot.

Solve the Problem RRR , When Designing a Road Is R=V2 g(f+tan⁡α)\mathrm { R } = \frac { \mathrm { V } ^ { 2 } } { \mathrm {~g} ( \mathrm { f } + \tan \alpha ) }R= g(f+tanα)V2​

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