Final answer:
The bank angle of a road for a car traveling at 40 m/s on a curve with a radius of 275 m can be calculated using the formula for an ideally banked curve without the need for friction.
Step-by-step explanation:
To find out at what angle a roadbed is banked for a car traveling at a certain speed on a curved path, we can use the principles of centripetal force and the concept of an ideally banked curve, where no friction is required to stay on the path. For a car traveling at 40 m/s on a banked road with a radius of curvature of 275 m, the banking angle θ can be found using the formula θ = tan-1(v2 / rg), where 'v' is the velocity, 'r' is the radius, and 'g' is the acceleration due to gravity (approximately 9.81 m/s2).
Plugging in the given values, we get θ = tan-1((40 m/s)2 / (275 m × 9.81 m/s2)) which can be calculated to find the banking angle.