Civil engineers generally bank, or angle, a curve on a road so that a car going around the curve at the recommended speed does not skid off the road. Engineers use this formula to calculate the proper banking angle, , where v represents the velocity in meters per second, r represents the radius of the curve in meters, and g represents the gravitational constant, 9.8 m/s2.
Tan ( = v2/rg
a. If the radius of an exit ramp is 60 m and the recommended speed is 40 km/h, at what angle should the curve be banked?
b. A curve on a racetrack is banked at 36°. The radius of the curve is about 1.7 km. What speed is this curve designed for?