A block slides down an incline of angle 30^circ with an acceleration of (9)/(4) where 'g' is acceleration due to gravity. Find the coefficient of kinetic friction. a 0.289 b 0.067 c Cannot be determined from the information given d 0.366

To find the coefficient of kinetic friction, we can use the equation:<br /><br />\[ \mu_k = \frac{g \sin(\theta) - a}{g \cos(\theta)} \]<br /><br />Given:<br />- Angle of the incline, \( \theta = 30^\circ \)<br />- Acceleration, \( a = \frac{9}{4}g \)<br />- Acceleration due to gravity, \( g \)<br /><br />Substitute the given values into the equation:<br /><br />\[ \mu_k = \frac{g \sin(30^\circ) - \frac{9}{4}g}{g \cos(30^\circ)} \]<br /><br />Simplify the equation:<br /><br />\[ \mu_k = \frac{g \cdot \frac{1}{2} - \frac{9}{4}g}{g \cdot \frac{\sqrt{3}}{2}} \]<br /><br />\[ \mu_k = \frac{\frac{1}{2}g - \frac{9}{4}g}{\frac{\sqrt{3}}{2}g} \]<br /><br />\[ \mu_k = \frac{\frac{2}{4}g - \frac{9}{4}g}{\frac{\sqrt{3}}{2}g} \]<br /><br />\[ \mu_k = \frac{-\frac{7}{4}g}{\frac{\sqrt{3}}{2}g} \]<br /><br />\[ \mu_k = \frac{-7}{4} \cdot \frac{2}{\sqrt{3}} \]<br /><br />\[ \mu_k = \frac{-7}{2\sqrt{3}} \]<br /><br />\[ \mu_k = -\frac{7}{2\sqrt{3}} \cdot \frac{\sqrt{3}}{\sqrt{3}} \]<br /><br />\[ \mu_k = -\frac{7\sqrt{3}}{6} \]<br /><br />Since the coefficient of kinetic friction cannot be negative, there must be an error in the given acceleration value. Therefore, the correct answer is:<br /><br />c) Cannot be determined from the information given