Final answer:
Maintaining an optimal RPM while driving uphill depends on the vehicle's power, the hill's steepness, the vehicle's load, and other efficiency factors. About 28 kW (37 hp) is often enough for a car to climb a gentle incline at 90 km/h, but specific RPM cannot be given without the exact vehicle details. It's generally best to keep the RPM modestly higher than on flat terrain to ensure consistent power delivery.
Step-by-step explanation:
The RPM (revolutions per minute) to maintain when driving uphill cannot be universally specified as it depends on various factors such as the vehicle's power, the incline's steepness, and the vehicle's load. From the provided information, we can determine that maintaining sufficient power is the key to successfully driving uphill. Using physics, we can calculate that approximately 28 kW (or about 37 hp) is reasonable for a car, weighing 1200 kg, to climb a gentle incline at 90 km/h while overcoming air resistance and friction. Given that an engine has a certain efficiency (for example, 25%), the power output needed could increase depending on the grade of the hill and additional forces such as friction.
Different cars will have varying power capabilities and thus will require different RPM ranges to maintain optimal power output while driving uphill. For example, climbing at 50 km/h on a maximum grade could require substantial power depending on the frictional forces. In real-world scenarios, factors like engine efficiency and thermal energy generation due to friction, which can be understood through the Second Law of Thermodynamics, will affect the amount of power your engine needs to exert. When on a steep climb like Pike's Peak, efficiency limitations mean you'd use more than the ideal energy for the trip.
Without knowing the exact specifications of the vehicle and the specific conditions of the incline, one cannot give a precise RPM to maintain. Generally, drivers are advised to keep their engines in a power band where the engine is neither struggling (low RPM) nor overexerting (high RPM), which usually means keeping the RPM slightly higher than usual to ensure the engine delivers steady power.