A car is traveling at 42.0 km/h on a flat highway.

(a) If the coefficient of friction between road and tires on a rainy day is 0.100, what is the minimum distance in which the car will stop?
m

(b) What is the stopping distance when the surface is dry and the coefficient of friction is 0.600?
m

To find the minimum stopping distance for a car, we need to consider the forces acting on the car. The main force responsible for stopping the car is the friction force between the tires and the road surface. The friction force is given by the equation:

Friction force = coefficient of friction * normal force

where the normal force is the force exerted by the road on the tires, which is equal to the weight of the car.

Let's calculate the answers to the given questions step by step:

(a) If the coefficient of friction between road and tires on a rainy day is 0.100, we need to find the minimum distance in which the car will stop.

1. Convert the speed from km/h to m/s:
Given speed = 42.0 km/h
1 km/h is equal to 0.2778 m/s (approximately)
So, the speed in m/s = 42.0 x 0.2778 = 11.66 m/s (approximately)

2. Calculate the deceleration:
Deceleration = v^2 / (2 * distance)
v is the initial velocity in m/s and distance is the distance the car travels until it comes to a stop.
Rearranging the equation, we have: distance = v^2 / (2 * deceleration)

3. Calculate the deceleration using the coefficient of friction:
Deceleration = coefficient of friction * g
Here, g is the acceleration due to gravity, approximately 9.8 m/s^2.

deceleration = 0.100 * 9.8 = 0.98 m/s^2

4. Plug in the values to find the minimum distance:
distance = (11.66^2) / (2 * 0.98) = 69.18 meters (approximately)

Therefore, the minimum distance in which the car will stop on a rainy day with a coefficient of friction of 0.100 is approximately 69.18 meters.

(b) If the surface is dry and the coefficient of friction is 0.600, we can use the same steps as above, but with a different coefficient of friction.

1. The speed in m/s remains the same: 11.66 m/s (approximately)

2. Calculate the deceleration:
deceleration = coefficient of friction * g
deceleration = 0.600 * 9.8 = 5.88 m/s^2

3. Plug in the values to find the stopping distance:
distance = (11.66^2) / (2 * 5.88) = 11.61 meters (approximately)

Therefore, the stopping distance when the surface is dry and the coefficient of friction is 0.600 is approximately 11.61 meters.