Introduction:
When an object falls freely under the influence of gravity, it experiences a force due to air resistance or friction. This force opposes the motion of the object and does work on it. In this scenario, we have an object of mass 4 kg dropped from a height of 20m, and it reaches the ground with a speed of 16m/s. We need to determine the work done on the body by air friction.

Calculating the initial potential energy:
The initial potential energy of the object can be calculated using the formula:
Potential Energy = mass × gravity × height
Potential Energy = 4 kg × 10 m/s² × 20 m
Potential Energy = 800 J

Calculating the final kinetic energy:
The final kinetic energy of the object can be calculated using the formula:
Kinetic Energy = 0.5 × mass × velocity²
Kinetic Energy = 0.5 × 4 kg × (16 m/s)²
Kinetic Energy = 0.5 × 4 kg × 256 m²/s²
Kinetic Energy = 512 J

Calculating the work done by air friction:
The work done by air friction can be calculated by subtracting the final kinetic energy from the initial potential energy:
Work Done = Potential Energy - Kinetic Energy
Work Done = 800 J - 512 J
Work Done = 288 J

Explanation:
When an object falls freely, its potential energy is converted into kinetic energy. In this case, the object has an initial potential energy of 800 J due to its position at a height of 20m. As it falls, it gains kinetic energy and reaches the ground with a speed of 16m/s, corresponding to a kinetic energy of 512 J.

The work done on the body by air friction is equal to the change in mechanical energy. In this case, the work done by air friction is the difference between the initial potential energy and the final kinetic energy, which is found to be 288 J. This work is negative because it acts against the motion of the object.

Hence, the work done on the body by air friction is 288 J.