Final answer:
The efficiency of a skier from top to bottom of a hill is determined by comparing the kinetic energy upon reaching the bottom to the potential energy at the top. The efficiency is calculated using energy conservation principles, though exact numeric values cannot be derived without the mass of the skier or consideration of non-conservative forces.
Step-by-step explanation:
The efficiency of a skier who starts from rest at the top of a 65m hill and has a speed of 23m/s upon reaching the bottom can be calculated using the conservation of energy principle and the concept of mechanical efficiency. Mechanical efficiency is the ratio of the useful work output to the total work input, and in this case, it relates the kinetic energy at the bottom of the hill to the potential energy at the top.
The total mechanical energy at the top is equal to the potential energy since the skier starts from rest, while the total mechanical energy at the bottom is the kinetic energy associated with the skier's velocity of 23m/s. The efficiency (η) can be found using the formula:
η = (Kinetic Energy at bottom / Potential Energy at top) × 100%
Kinetic Energy at bottom = 0.5 × mass × velocity2
Potential Energy at top = mass × gravity × height
Since the mass of the skier is not provided, we cannot compute a numeric answer, but we can express the efficiency in terms of mass (m), which would cancel out, showing that the efficiency is independent of the mass of the skier. We would need additional information about non-conservative forces like friction and air resistance to make a complete analysis, as these affect the actual efficiency.