(Modeling) Solve each problem. Speed Limit on a Curve Refer to Exerci...

(Modeling) Solve each problem.

Speed Limit on a Curve Refer to Exercise 67 and use the same values for ƒ and g. A highway curve has radius R = 1150 ft and a superelevation of θ = 2.1°. What should the speed limit (in miles per hour) be for this curve?

(Reference Exercise 67)

Design of Highway Curves When highway curves are designed, the outside of the curve is often slightly elevated or inclined above the inside of the curve. See the figure. This inclination is the superelevation. For safety reasons, it is important that both the curve’s radius and superelevation be correct for a given speed limit. If an automobile is traveling at velocity V (in feet per second), the safe radius R for a curve with superelevation u is modeled by the formula

.

where f and g are constants. (Source: Mannering, F. and W. Kilareski, Principles of Highway Engineering and Traffic Analysis, Second Edition, John Wiley and Sons.)

(a) A roadway is being designed for automobiles traveling at 45 mph. If θ = 3 °, g = 32.2 , and ƒ = 0.14 , calculate R to the nearest foot. (Hint: 45 mph 5 66 ft per sec)

(b) Determine the radius of the curve, to the nearest foot, if the speed in part (a) is increased to 70 mph.

(c) How would increasing the angle u affect the results? Verify your answer by repeating parts (a) and (b) with θ = 4 °.