A cyclist speeding at `6ms^(-1)` in a circle of 18 m radius makes an angle `theta `with the vertical. Calculate `theta`. Also determine the minimum possible value of the coefficient of friction between the tyres and the ground?

Explanation

To solve the problem step by step, we will follow the physics principles related to circular motion and the banking of roads.

### Step 1: Understand the problem
We have a cyclist moving in a circular path with a speed of \( v = 6 \, \text{m/s} \) and a radius of \( r = 18 \, \text{m} \). We need to find the angle \( \theta \) that the cyclist makes with the vertical and the minimum coefficient of friction \( \mu \) required for this motion.

### Step 2: Use the formula for banking angle
For a banked curve, the relationship between the banking angle \( \theta \), speed \( v \), radius \( r \), and acceleration due to gravity \( g \) is given by:
\[
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