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Introduction:
The work done by the drag force of the air on a body can be calculated by using the work-energy principle. In this case, a body of mass 10kg is released from the top of a tower and falls through a distance of 20m, acquiring a velocity of 10m/s. We need to determine the work done by the drag force of the air on the body.

Work-Energy Principle:
The work-energy principle states that the work done on an object is equal to the change in its kinetic energy. Mathematically, it can be expressed as:

W = ΔKE

Where W is the work done, ΔKE is the change in kinetic energy.

Calculation:
1. Calculate the initial potential energy (PE) of the body.
PE = mgh
where m is the mass of the body, g is the acceleration due to gravity, and h is the height of the tower.
In this case, m = 10kg, g = 9.8m/s², and h = 20m.
PE = 10kg * 9.8m/s² * 20m = 1960 Joules

2. Calculate the final kinetic energy (KE) of the body.
KE = 0.5mv²
where m is the mass of the body and v is the final velocity of the body.
In this case, m = 10kg and v = 10m/s.
KE = 0.5 * 10kg * (10m/s)² = 500 Joules

3. Calculate the work done by the drag force of the air.
W = ΔKE
= KE - PE
= 500 Joules - 1960 Joules
= -1460 Joules (negative sign indicates work done against the direction of motion)

Explanation:
The negative value of work (-1460 Joules) indicates that the drag force of the air is doing work against the motion of the body. This means that the air resistance is acting in the opposite direction to the motion of the body, causing a decrease in its kinetic energy. The work done by the drag force of the air can be thought of as the energy dissipated due to air resistance.