A highway curve in the horizontal plane is banked so that vehicles can proceed safely
even if the road is slippery. Determine the proper banking angle for a car travelling at
97 km/h on a curve of radius 450 m.
To determine the proper banking angle for the curve, we can use the following equation:
tan(theta) = (v^2) / (r * g)
where:
theta = banking angle
v = velocity of the car (97 km/h = 26.94 m/s)
r = radius of the curve (450 m)
g = acceleration due to gravity (9.81 m/s^2)
Plugging in the values, we get:
tan(theta) = (26.94^2) / (450 * 9.81)
tan(theta) = 675.96 / 4419.5
theta = arctan(0.1528)
theta ≈ 8.74 degrees
Therefore, the proper banking angle for a car travelling at 97 km/h on a curve of radius 450 m is approximately 8.74 degrees.