1. **Stating the problem:** We need to find the acceleration of a rock sliding down an inclined plane and the coefficient of friction between the rock and the plane. 2. **Formulas and important rules:** - The acceleration $a$ of an object sliding down an incline with friction is given by: $$a = g(\sin\theta - \mu \cos\theta)$$ where $g$ is acceleration due to gravity, $\theta$ is the angle of the incline, and $\mu$ is the coefficient of friction. - The frictional force opposes motion and is $f = \mu N$, where $N = mg\cos\theta$ is the normal force. 3. **Intermediate work:** - Rearranging the formula to find $\mu$ if acceleration $a$ is known: $$a = g\sin\theta - \mu g\cos\theta$$ $$\mu g\cos\theta = g\sin\theta - a$$ $$\mu = \frac{g\sin\theta - a}{g\cos\theta}$$ 4. **Explanation:** - To find acceleration, we need the angle $\theta$ and coefficient $\mu$ or vice versa. - If acceleration is measured, use the above formula to find $\mu$. - If $\mu$ is known, plug into the acceleration formula. 5. **Final answers:** - Acceleration: $$a = g(\sin\theta - \mu \cos\theta)$$ - Coefficient of friction: $$\mu = \frac{g\sin\theta - a}{g\cos\theta}$$ Note: To provide numerical answers, values for $\theta$, $a$, and $g$ are needed.