Final answer:
The correct new radius of curvature to increase the speed by 10% while maintaining the same banking angle would be approximately 16.53m, which is not listed in the given options.
Step-by-step explanation:
The question pertains to the relationship between the banking angle, radius of curvature, and speed with which a car can safely travel on a banked curve. According to the question, we are to keep the banking angle constant and determine the new radius of curvature required to increase the maximum speed by 10%. The relationship between these variables in a frictionless scenario is given by the formula: v^2 = r*g*tan(θ), where v is the speed of the car, r is the radius of curvature, g is the acceleration due to gravity, and θ is the banking angle of the road.
To find the solution, we can set up the proportionality that follows from the above equation if the angle and acceleration due to gravity are constants: v1^2 / r1 = v2^2 / r2. Given that the speed is to be increased by 10%, meaning v2 = 1.1 * v1, we can solve for the new radius r2 by algebraically manipulating the equation to isolate r2:
r2 = (v1^2 / v2^2) * r1
= (1 / (1.1^2)) * 20m
= 20m / 1.21
= 16.53m
None of the given options exactly match this calculated value, so there may be a discrepancy or mistake in the options provided. In reality, if one were to increase the speed by 10% while keeping the banking angle the same, the radius would need to be about 16.53 meters to maintain the same dynamics.