What is the maximum speed with which a cylist can turn around curved path of radius 10.0 m, if the coefficient of friction between the tyre and the road is 0.5 ? If the cyclist wants to avoid overturning by what angle the cyclist must lean from the vertical ?

Explanation

To solve the problem step by step, we will break it down into two parts: finding the maximum speed of the cyclist and determining the angle at which the cyclist must lean to avoid overturning.

### Part 1: Maximum Speed Calculation

1. **Identify the forces acting on the cyclist**:
- The gravitational force acting downwards: \( F_g = mg \)
- The normal force acting perpendicular to the road: \( R \)
- The frictional force providing the centripetal force: \( F_f = \mu R \)
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