Final answer:
The work done by air resistance on a skydiver with a constant velocity is -2.93 × 10⁵ J, as the air resistance force is equal but opposite to the gravitational force, and work is calculated as force times distance in the direction of the force.
Step-by-step explanation:
The work done by a nonconservative force such as air resistance can be calculated as the product of the force and the distance over which it acts, in the direction of the force. Since the skydiver is falling with a constant velocity, the force of air resistance must be equal and opposite to the gravitational force acting on the skydiver, resulting in no net force and therefore no acceleration. The work done by air resistance is thus equal to the gravitational force times the distance fallen, with a negative sign because the force of air resistance acts in the opposite direction to the displacement.
First, we need to calculate the gravitational force acting on the skydiver:
F_gravity = mass × acceleration due to gravity
F_gravity = 92.0 kg × 9.8 m/s²
F_gravity = 901.6 N
Now, we can calculate the work done by air resistance:
Work = force × distance × cos(ϸ)
Since the angle (ϸ) between the force of air resistance and the direction of displacement is 180 degrees (opposite directions), cos(ϸ) is -1. Therefore:
Work = -901.6 N × 325 m × -1
Work = -2.93 × 10⁵ J
The correct answer is D) -2.93 times 10⁵ J, which means the work done by air resistance is negative because it acts in the direction opposite to the displacement.