On an icy day, you worry about parking your car in your driveway, which has an incline of 12º. Your neighbor's driveway has an incline of 9.0º, and the driveway across the street is at 6.0º. The coefficient of static friction between tire rubber and ice is 0.15. Which driveway(s) will be safe to park in?

Driveway across the street () is the only choice for a safe parking.

Explanation:

Let suppose that car is represented by a particle, then we proceed to construct its free body diagram and corresponding equations of equilibrium:

(Eq. 1)

(Eq. 2)

Where:

- Static friction force, measured in newtons.

- Normal force on the car from the ground, measured in newtons.

- Weight of the car, measured in newtons.

- Driveway inclination, measured in sexagesimal degrees.

By applying definitions of maximum static friction force and weight, we expand the system of equations presented above:

(Eq. 1b)

(Eq. 2b)

Where:

- Static coefficient of friction, dimensionless.

- Mass of the car, measured in kilograms.

- Gravitational acceleration, measured in meters per square second.

Then, we substitute normal force and simplify the resulting expression:

(Eq. 3)

Based on such result, we can conclude that if driveway inclination is greater than value reported, then car shall not be safe in case of parking. Our reference angle is: ()

By direct comparison, we find that driveway across the street () is the only choice for a safe parking.

the answer is b ) square root of 5