A 1500 kg automobile travels at a speed of 105 km/h along a straight concrete highway. Faced with an emergency situation, the driver jams on the brakes, and the car skids to a stop.

(a) What will be the car's stopping distance for dry pavement (µ = 0.85)?
(b) What will be the car's stopping distance for wet pavement (µ = 0.60)?

To find the car's stopping distance, we need to use the equation of motion that relates the stopping distance to the initial velocity, the coefficient of friction, and other factors.

The equation for stopping distance is:
Stopping Distance = (Initial Velocity^2) / (2 * Acceleration)

First, let's find the acceleration of the car. The net force acting on the car during the skid is given by:
Net Force = frictional force = coefficient of friction * normal force

The normal force is equal to the weight of the car, which we can find using the formula:
Weight = mass * gravity

The acceleration of the car can be obtained using Newton's second law:
Net Force = mass * acceleration

Now, let's calculate the stopping distance for dry pavement (µ = 0.85):
(a) Taking the coefficient of friction as 0.85, we start by finding the normal force:
Weight = (1500 kg) * (9.8 m/s^2) = 14700 N (Newtons)

Next, we calculate the net force:
Net Force = (0.85) * (14700 N) = 12495 N

Then, we calculate the acceleration:
12495 N = (1500 kg) * a
a = 8.33 m/s^2

Finally, we substitute the values into the stopping distance equation:
Stopping Distance = (105 km/h) * (1000 m/km) * (1 h/3600 s) * (1 m/s) / (2 * 8.33 m/s^2)
Stopping Distance = 36.75 meters

Therefore, the car's stopping distance for dry pavement is 36.75 meters.

Now, let's calculate the stopping distance for wet pavement (µ = 0.60):
(b) Taking the coefficient of friction as 0.60, we start again by finding the normal force:
Weight = (1500 kg) * (9.8 m/s^2) = 14700 N (Newtons)

Next, we calculate the net force:
Net Force = (0.60) * (14700 N) = 8820 N

Then, we calculate the acceleration:
8820 N = (1500 kg) * a
a = 5.88 m/s^2

Finally, we substitute the values into the stopping distance equation:
Stopping Distance = (105 km/h) * (1000 m/km) * (1 h/3600 s) * (1 m/s) / (2 * 5.88 m/s^2)
Stopping Distance = 57.55 meters

Therefore, the car's stopping distance for wet pavement is 57.55 meters.