Consider again the problem of a car traveling along a banked turn. Sometimes roads have a "reversed" banking angle. That is, the road is tilted "away" from the center of curvature of the road. If the coefficient of static friction between the tires and the road is ìs = 0.4, the radius of curvature is 13 m, and the banking angle is 7°, what is the maximum speed at which a car can safely navigate such a turn?

To determine the maximum speed at which a car can safely navigate a turn with a reversed banking angle, we need to find the speed at which the car's frictional force is equal to the centripetal force required to stay in a circular path.

To start, let's draw a free-body diagram of the car on a banked turn:

1. Identify the forces acting on the car:
- The weight of the car acting vertically downwards (mg), where m is the mass of the car and g is the acceleration due to gravity.
- The normal force (N) acting perpendicular to the surface of the road.
- The frictional force (f) acting parallel to the surface of the road, opposing the component of weight that is perpendicular to the road.
- The centripetal force (Fc) acting toward the center of the curvature.

2. Resolve the weight of the car:
The weight of the car can be resolved into two components: the component perpendicular to the road's surface (mg * cosθ) and the component parallel to the road's surface (mg * sinθ), where θ is the banking angle.

3. Determine the normal force:
The normal force is equal to the component of weight perpendicular to the road's surface. Therefore, N = mg * cosθ.

4. Calculate the frictional force:
The frictional force can be determined using the formula f = μs * N, where μs is the coefficient of static friction.

5. Determine the centripetal force:
The centripetal force is given by Fc = (mv^2) / r, where m is the mass of the car, v is the velocity of the car, and r is the radius of curvature.

6. Set up the equation:
Equating the frictional force and the centripetal force, we have μs * N = (mv^2) / r.

7. Solve for the velocity (v):
Rearrange the equation to solve for v:
v = √(μs * g * r * tanθ)

8. Plug in the known values:
Given:
μs = 0.4
m (mass) - not given
g (acceleration due to gravity) = 9.8 m/s^2
r (radius of curvature) = 13 m
θ (banking angle) = 7°

Plug in the values into the equation and calculate the maximum speed at which the car can safely navigate the turn.