To determine the required power for a cable car on a slope, first calculate the change in height, which is essential for understanding energy changes. The cable car, moving up a 1000 m slope at a 30-degree angle and a speed of 3.5 m/s, carries 20 persons with an average weight of 600 N each. Work is needed to lift the cable car, and this can be calculated using the height change and the total weight. The time taken to ascend the slope can be derived from the speed and distance, allowing for the calculation of power using the formula Power = Work/Time. Overall, the problem emphasizes the relationship between work, energy changes, and the required power for the cable car operation.