Given,
The coefficient of friction between the wheel and the road, μ=0.4
The radius of curvature of the road, r=100 m
The centripetal force for the cyclist to move in the curved path is provided by the friction between the road and the wheel.
Thus,
[tex]\begin{gathered} \frac{mv^2}{r}=\mu mg \\ \Rightarrow v^2=r\mu g \\ v=\sqrt[]{r\mu g} \end{gathered}[/tex]Where m is the mass of the cyclist and the cycle and g is the acceleration due to gravity.