Final answer:
To find the velocity of the car at the top of the hill, we first calculate the gravitational potential energy and then convert it into kinetic energy. The velocity of the car is approximately 26.52 m/s.
Step-by-step explanation:
In order to answer this question, we need to determine the gravitational potential energy of the car at the top of the hill and convert it into kinetic energy. The gravitational potential energy is given by the formula GPE = mgh, where m is the mass of the car, g is the acceleration due to gravity, and h is the height of the hill. Since the car is driving over the top of the hill, its height can be considered as the radius of the hill.
First, we can calculate the gravitational potential energy:
GPE = (1500 kg)(9.8 m/s^2)(12.0 m) = 176,400 J
Next, we can convert this energy into kinetic energy, using the formula KE = 1/2mv^2, where v is the velocity of the car. Rearranging the formula to solve for velocity, we get:
v = sqrt((2 * KE) / m)
Substituting the values, we can calculate the velocity of the car:
v = sqrt((2 * 176400 J) / 1500 kg) = 26.52 m/s
Therefore, the velocity of the car at the top of the hill is approximately 26.52 m/s.