What is the Maximum Speed of a Car at the Top of a Hill?

The video tutorial explores the physics problem of determining the maximum linear speed a car can achieve over a semicircular hill without its tires lifting off the ground. The problem is approached by analyzing the forces acting on the car using a free body diagram, focusing on the normal force and gravitational force. The tutorial derives the equation for maximum speed by setting the normal force to zero, ensuring the car maintains contact with the ground. The final calculation shows that the maximum speed is 4.2 meters per second, independent of the car's mass, depending only on gravitational acceleration and the hill's radius.

How is the maximum speed related to the gravitational force and the radius of the hill?

Why is the maximum speed independent of the mass of the vehicle?