A car attempts to accelerate up a hill at an angle $\theta$ to the horizontal. The coefficient of static friction between the tires and the hill is $\mu > \tan \theta$. What is the maximum acceleration the car can achieve (in the direction upwards along the hill)? Neglect the rotational inertia of the wheels.

(A) $g \tan \theta$
(B) $g(\mu \cos \theta - \sin \theta)$
(C) $g(\mu - \sin \theta)$
(D) $g \mu \cos \theta$
(E) $g(\mu \sin \theta - \cos \theta)$
To determine the maximum acceleration the car can achieve while moving up the hill, we need to analyze the forces acting on the car. The forces involved are:

1. The gravitational force acting downwards, which has a component along the hill.
2. The normal force perpendicular to the hill.
3. The frictional force, which opposes the motion and acts up the hill.

Let's break down the forces and solve for the maximum acceleration.

1. **Gravitational Force Components:**
   - The gravitational force $mg$ can be decomposed into two components:
     - Parallel to the hill: $mg \sin \theta$
     - Perpendicular to the hill: $mg \cos \theta$

2. **Normal Force:**
   - The normal force $N$ is equal to the perpendicular component of the gravitational force:
     \[
     N = mg \cos \theta
     \]

3. **Frictional Force:**
   - The maximum static frictional force $f_{\text{max}}$ is given by:
     \[
     f_{\text{max}} = \mu N = \mu mg \cos \theta
     \]

4. **Net Force and Acceleration:**
   - The net force $F_{\text{net}}$ acting up the hill is the difference between the frictional force and the component of the gravitational force parallel to the hill:
     \[
     F_{\text{net}} = f_{\text{max}} - mg \sin \theta
     \]
   - Substituting the expressions for $f_{\text{max}}$ and simplifying:
     \[
     F_{\text{net}} = \mu mg \cos \theta - mg \sin \theta
     \]
   - The net force is also equal to the mass of the car times its acceleration $a$:
     \[
     F_{\text{net}} = ma
     \]
   - Therefore, the maximum acceleration $a$ is:
     \[
     ma = \mu mg \cos \theta - mg \sin \theta
     \]
     \[
     a = g (\mu \cos \theta - \sin \theta)
     \]

Thus, the maximum acceleration the car can achieve while moving up the hill is given by:
\[
\boxed{g (\mu \cos \theta - \sin \theta)}
\]