Introduction:
In order to increase the maximum safe speed of a passing vehicle, the radius of curvature of the road needs to be adjusted. By keeping the banking angle constant and following certain guidelines, we can determine the new radius of curvature required.

Understanding the Problem:
The problem states that the maximum safe speed of a passing vehicle needs to be increased by 10%. This means that the vehicle should be able to navigate the curve at a higher speed without losing control or skidding. To achieve this, we need to adjust the radius of curvature of the road.

Analysis:
To analyze the situation, we need to consider the concept of banking angle. The banking angle is the angle at which the road is inclined or tilted towards the inside of the curve. It helps to provide an extra force, known as the banking force, which assists the vehicle in turning smoothly.

Formula:
The formula to calculate the banking angle is:
tanθ = (v^2) / (g * r)

where:
θ = banking angle
v = velocity of the vehicle
g = acceleration due to gravity
r = radius of curvature of the road

Adjusting the Radius of Curvature:
To increase the maximum safe speed by 10%, we need to adjust the radius of curvature. We can rearrange the formula to solve for the new radius of curvature:

r' = (v^2) / (g * tanθ')

where:
r' = new radius of curvature
v = velocity of the vehicle
g = acceleration due to gravity
θ' = new banking angle

Calculation:
1. Let's assume the initial radius of curvature is 20m.
2. We can use this value to calculate the initial banking angle using the formula mentioned earlier.
3. Once we have the initial banking angle, we can calculate the new banking angle by increasing it by 10%.
4. Using the new banking angle and the initial velocity, we can calculate the new radius of curvature using the rearranged formula.

Conclusion:
By adjusting the radius of curvature of the road based on the given parameters and using the formula for banking angle, we can determine the new radius of curvature required to increase the maximum safe speed of a passing vehicle by 10%. This will help ensure that the vehicle can navigate the curve safely at a higher speed without any skidding or loss of control.