The minimum coefficient of static friction between the pavement and the tires is 0.69.
The given parameters;
The normal force on the car is calculated as follows;
[tex]F_n = mgcos(\theta)[/tex]
The frictional force between the car and the road is calculated as;
[tex]F_k = \mu_k F_n\\\\F_k = \mu_k mgcos(\theta)[/tex]
The net force on the car is calculated as follows;
[tex]mgsin(\theta) + \mu_s mgcos(\theta) = \frac{mv^2}{r} \\\\mg(sin\theta \ + \ \mu_s cos\theta)= \frac{mv^2}{r} \\\\g(sin\theta \ + \ \mu_s cos\theta)= \frac{v^2}{r}\\\\sin\theta \ + \ \mu_s cos\theta = \frac{v^2}{rg}\\\\\mu_s cos\theta = sin\theta \ + \ \frac{v^2}{rg}\\\\\mu_s = \frac{sin\theta}{cos \theta} + \frac{v^2}{cos (\theta)rg}\\\\\mu_s = tan(\theta) + \frac{v^2}{cos (\theta)rg}\\\\\mu_s = tan(10.8) + \frac{(20.83)^2}{cos(10.8) \times 90 \times 9.8} \\\\\mu_s = 0.19 + 0.5\\\\[/tex]
[tex]\mu_s = 0.69[/tex]
Thus, the minimum coefficient of static friction between the pavement and the tires is 0.69.
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