Final answer:
The car's total energy at the top of the 10-meter hill, considering both its kinetic energy and gravitational potential energy, is 596,000 Joules.
Step-by-step explanation:
A 2000-kg car is driving along a road at 20 m/s and has reached the top of a 10-meter hill. To calculate the car's total energy, we need to consider both its kinetic energy (KE) and gravitational potential energy (GPE). The kinetic energy can be calculated using the formula: KE = (1/2)mv², where m is the mass in kilograms and v is the velocity in meters per second. The gravitational potential energy is given by the formula: GPE = mgh, where m is the mass, g is the acceleration due to gravity (9.8 m/s² on Earth), and h is the height in meters.
First, we calculate the kinetic energy for the car: KE = (1/2) * 2000 kg * (20 m/s)² = 400,000 J (Joules).
Next, we calculate the gravitational potential energy: GPE = 2000 kg * 9.8 m/s² * 10 m = 196,000 J.
Finally, we add the two to get the total energy: Total Energy = KE + GPE = 400,000 J + 196,000 J = 596,000 J. Therefore, the car's total energy at the top of the hill is 596,000 Joules.