Physics Problem: Work, Energy and Power for an Uphill Skier

Solve a challenging physics problem involving work, energy, and power for an uphill skier. Calculate the power output required to overcome gravitational force and air resistance for a 75.0-kg cross-country skier climbing a 3.0º slope at a constant speed of 2.00 m/s with 25.0 N of air resistance. Determine the average force exerted backward on the snow to achieve this motion. Finally, analyze how long it would take the skier to reach a velocity of 10.0 m/s on level ground while maintaining the same force and air resistance. This problem-solving exercise, based on the OpenStax College Physics textbook, offers practical application of fundamental physics concepts in a real-world scenario.