## Rolling Down a Hill Again

Consider two cars are at the same starting positions at the top of a hill. Car A has all the passengers in the front seats, while Car B has all the passengers in the back seats (same mass, just different weight distributions). If both cars were to simultaneously start rolling downward, which one would typically reach the bottom of the hill first? Why? Assume all environmental and design attributes are identical for both cars.

Hint
Law of Conservation of Energy:
$$KE_1+PE_1=KE_2+PE_2$$$where $$KE_1$$ is the initial kinetic energy, $$PE_1$$ is the initial potential energy, $$KE_2$$ is the final kinetic energy, and $$PE_2$$ is the final potential energy. Hint 2 Remember, gravitational potential energy is: $$PE=mass\times gravity\times height$$$
Assuming all environmental and design attributes are identical, Car B with all the passengers in the back seat should reach the hill's bottom first due to greater potential energy at the start. The question is testing our understanding of the Conservation of Energy Law:
$$KE_1+PE_1=KE_2+PE_2$$$where $$KE_1$$ is the initial kinetic energy, $$PE_1$$ is the initial potential energy, $$KE_2$$ is the final kinetic energy, and $$PE_2$$ is the final potential energy. At the top of the hill, the kinetic energy is zero, while potential energy is maximized. Due to conservation of energy, the potential energy will linearly convert to kinetic energy as the cars roll down the hill until they reach the bottom (assuming no heat loss). At the hill's bottom, potential energy is zero, while kinetic energy is maximized. The car with the greatest kinetic energy at the end will reach the bottom first. Remember, gravitational potential energy is: $$PE=mass\times gravity\times height$$$
Car B has a larger starting height due to the passengers in the back seat (where is the mass situated?), which equates to a greater initial potential energy. The bigger potential energy translates to greater final kinetic energy.
Car B due to greater potential energy.