Final answer:
The work done by air resistance is calculated as the difference between the gravitational potential energy lost and the kinetic energy gained by the ball, applying the conservation of energy principle along with the known values of mass, height, and speed.
Step-by-step explanation:
The work done by air resistance on a falling object can be calculated using the principle of conservation of energy. Given a 5 kg ball falls through a height of 20 meters and acquires a speed of 10 meters per second, compared to what it would have attained in the absence of air resistance (based on gravitational acceleration), the work done by air can be found by the difference in kinetic energies.
First, calculate the potential energy lost by the ball: Gravitational Potential Energy (GPE) = mass × gravitational acceleration (g) × height (h) = 5 kg × 9.8 m/s² × 20 m. Then, find the kinetic energy gained by the ball: Kinetic Energy (KE) = 0.5 × mass × velocity² = 0.5 × 5 kg × (10 m/s)². The work done by air resistance is the difference between the GPE lost and the KE gained.
Calculation: Work done by air resistance = GPE - KE.