# What is the Ideal Banking Angle for a Gentle Turn on a Highway?

## Calculation of Ideal Banking Angle

In order to determine the ideal banking angle for a gentle turn of 1.50 km radius on a highway with a speed limit of 115 km/h, we can use the following formula:

**Banking Angle** = tan^{-1}(v^{2} / (g * r))

Where:

**Banking Angle**is the angle at which the road is banked in degrees**v**is the velocity of the car (in m/s)**g**is the acceleration due to gravity (9.8 m/s^{2})**r**is the radius of the turn (in meters)

## Given Data:

Radius of the turn, **r** = 1.50 km = 1500 m

Speed limit, **v** = 115 km/h = 31.9 m/s

## Calculation:

Substitute the given values into the formula:

**Banking Angle** = tan^{-1}((31.9 m/s)^{2} / (9.8 m/s^{2} * 1500 m))

Simplify the equation:

**Banking Angle** = tan^{-1}(3251.61 / 14700)

Using a calculator, we find:

**Banking Angle** ≈ 12.63°

Therefore, the ideal banking angle for a gentle turn of 1.50 km radius on a highway with a speed limit of 115 km/h is approximately **12.63 degrees.**