Step 1: Identify the forces acting on the block. The forces acting on the block are: • Gravitational force ($mg$) acting vertically downwards. • Normal force ($N$) acting perpendicular to the inclined plane. • Kinetic frictional force ($f_k$) acting parallel to the inclined plane, opposing the motion (up the plane). Step 2: Resolve the gravitational force into components parallel and perpendicular to the inclined plane. The component of gravitational force parallel to the plane is $mg \sin\theta$. The component of gravitational force perpendicular to the plane is $mg \cos\theta$. Step 3: Apply Newton's Second Law in the direction perpendicular to the plane. Since there is no acceleration perpendicular to the plane, the net force in this direction is zero. $$ \sum F_\perp = N - mg \cos\theta = 0 $$ Therefore, the normal force is: $$ N = mg \cos\theta $$ Step 4: Calculate the kinetic frictional force. The kinetic frictional force is given by $f_k = \mu_k N$. Substitute the expression for $N$: $$ f_k = \mu_k (mg \cos\theta) $$ Step 5: Apply Newton's Second Law in the direction parallel to the plane. The block is sliding down the plane, so the net force down the plane causes the acceleration. $$ \sum F_\parallel = mg \sin\theta - f_k = ma $$ Substitute the expression for $f_k$: $$ mg \sin\theta - \mu_k mg \cos\theta = ma $$ Step 6: Solve for the acceleration ($a$). Divide the entire equation by $m$: $$ a = g \sin\theta - \mu_k g \cos\theta $$ Factor out $g$: $$ a = g (\sin\theta - \mu_k \cos\theta) $$ Step 7: Substitute the given values and calculate the acceleration. Given: $m = 2.0 \text{ kg}$ $\theta = 30^\circ$ $\mu_k = 0.20$ $g = 9.8 \text{ m/s}^2$ (standard acceleration due to gravity) $$ a = 9.8 \text{ m/s}^2 (\sin(30^\circ) - 0.20 \cos(30^\circ)) $$ We know that $\sin(30^\circ) = 0.5$ and $\cos(30^\circ) = \frac{\sqrt{3}}{2} \approx 0.866$. $$ a = 9.8 \text{ m/s}^2 (0.5 - 0.20 \times 0.866) $$ $$ a = 9.8 \text{ m/s}^2 (0.5 - 0.1732) $$ $$ a = 9.8 \text{ m/s}^2 (0.3268) $$ $$ a \approx 3.20264 \text{ m/s}^2 $$ Rounding to two significant figures: $$ a \approx 3.2 \text{ m/s}^2 $$ The acceleration of the block is $\boxed{\text{3.2 m/s}^2}$. That's 2 down. 3 left today — send the next one.