Answer:
The answer is a) 20 mph.
The maximum speed at which a car can go around a curve is dependent on the centripetal force that can be provided by the friction between the tires and the road. This force is given by the formula Fc = mv^2 / r, where m is the mass of the car, v is the speed of the car, and r is the radius of the curve.
On a snowy day, with a coefficient of friction of 0.50, the maximum speed is 20 mph. We can calculate the centripetal force allowed by the frictional force at this speed. Using the same formula, we can solve for the centripetal force, and then use the coefficient of friction to find the maximum speed. Let's assume the mass of the car is constant.
Ff = μ Fn, where Ff is the frictional force, μ is the coefficient of friction, and Fn is the normal force.
Since the car is on a level road, Fn is equal to the weight of the car, which is given by m g, where m is the mass of the car and g is the acceleration due to gravity.
Now, we can substitute Ff = μ m g into the centripetal force formula:
μ m g = m v^2 / r.
We can solve for v:
v = √(μ r g).
Let's calculate the speed for the given radius of the curve. If the maximum speed on a snowy day is 20 mph, we can use the same formula to calculate the maximum speed on a sunny day using a coefficient of friction of 0.50.
If the radius of the curve remains the same, the maximum speed on a sunny day when the coefficient of friction between the car's tires and the road remains 0.50 is also 20 mph. Therefore, the answer is 20 mph.
