1. **State the problem:** We need to find the smallest radius $R$ of a horizontal circular track on which a car can travel at velocity $v=15$ m/s without skidding, given the coefficient of friction $\mu=0.3$. 2. **Relevant formula:** The frictional force provides the centripetal force needed to keep the car moving in a circle without skidding. The maximum frictional force is $f_{max} = \mu mg$. The centripetal force required is $F_c = \frac{mv^2}{R}$. For the car not to skid, the maximum frictional force must be at least equal to the centripetal force: $$\mu mg \geq \frac{mv^2}{R}$$ 3. **Simplify the inequality:** Cancel mass $m$ from both sides: $$\mu g \geq \frac{v^2}{R}$$ Rearranged to solve for $R$: $$R \geq \frac{v^2}{\mu g}$$ 4. **Substitute known values:** Given $v=15$ m/s, $\mu=0.3$, and $g=9.8$ m/s$^2$: $$R \geq \frac{15^2}{0.3 \times 9.8}$$ Calculate numerator and denominator: $$R \geq \frac{225}{2.94}$$ 5. **Calculate the radius:** $$R \geq 76.53$$ 6. **Interpretation:** The smallest radius the car can travel without skidding is approximately 76.53 meters. **Final answer:** $$\boxed{R \approx 76.5 \text{ meters}}$$