Question

A banked highway is designed for traffic moving at 90.0 km/h. The radius of the curve is 310 m. What is the angle of banking of the highway?

a) 23.3 degrees
b) 25.7 degrees
c) 28.1 degrees
d) 31.6 degrees

Answer 1

The angle of banking of the highway is approximately 23.3 degrees.

Step-by-step explanation:

To determine the angle of banking of the highway, we can use the formula:

tanθ = (v^2)/(r*g)

where θ is the angle of banking, v is the velocity of traffic, r is the radius of the curve, and g is the acceleration due to gravity. Plugging in the given values:

tanθ = ((90 km/h)^2)/(310 m * 9.8 m/s^2)

Solving for θ:

θ = arctan((90 km/h)^2/(310 m * 9.8 m/s^2))

θ ≈ 23.3 degrees

Therefore, the angle of banking of the highway is approximately 23.3 degrees (option a).