For traffic moving at `60km//h` if the radius of the curve is `0.1km` what is the correct angle of banking of the road Given `g = 10m//s^(2)` .

Explanation

To find the correct angle of banking of the road for traffic moving at 60 km/h with a radius of 0.1 km, we can follow these steps:

### Step 1: Convert the speed from km/h to m/s
The speed given is 60 km/h. To convert this to meters per second (m/s), we use the conversion factor:
\[ \text{Speed (m/s)} = \frac{\text{Speed (km/h)}}{3.6} \]
Calculating this gives:
\[ \text{Speed} = \frac{60}{3.6} = 16.67 \, \text{m/s} \]

### Step 2: Identify the radius in meters
The radius of the curve is given as 0.1 km. We convert this to meters:
\[ \text{Radius} = 0.1 \, \text{km} = 100 \, \text{m} \]

### Step 3: Use the formula for the angle of banking
The formula for the tangent of the banking angle \(\theta\) is given by:
\[ \tan \theta = \frac{v^2}{rg} \]
Where:
- \(v\) is the speed in m/s,
- \(r\) is the radius in meters,
- \(g\) is the acceleration due to gravity (given as \(10 \, \text{m/s}^2\)).

### Step 4: Substitute the values into the formula
Substituting the values we have:
\[ \tan \theta = \frac{(16.67)^2}{100 \times 10} \]
Calculating \(v^2\):
\[ v^2 = (16.67)^2 = 278.0889 \, \text{m}^2/\text{s}^2 \]
Now substituting this into the equation:
\[ \tan \theta = \frac{278.0889}{1000} = 0.2780889 \]

### Step 5: Calculate the angle \(\theta\)
To find \(\theta\), we take the arctangent (inverse tangent) of the result:
\[ \theta = \tan^{-1}(0.2780889) \]
Using a calculator, we find:
\[ \theta \approx 15.5^\circ \]

### Final Answer
The correct angle of banking of the road is approximately \(15.5^\circ\).

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