a skydiver is subject to two forces: gravity and air resistance. Falling vertically, she reaches a constant terminal speed at some time after jumping from the plane. Since she is moving at a constant velocity from that time until her chute opens, we conclude from the work kinetic energy theorem that, over that time interval,

A. The work done by gravity equals the negative of the work done by the air resistance.
B. The work done by gravity is zero.
C. The work done by gravity equals the work done by air resistance.
D. The work done by air resistance is 0.
E. Her kinetic energy increases.

Please help me with this...

To determine the correct answer, let's analyze the forces acting on the skydiver during the time interval when she reaches terminal velocity until her chute opens.

1. Gravity: Gravity is a downward force acting on the skydiver throughout the entire fall. Its magnitude is given by the mass of the skydiver multiplied by the acceleration due to gravity (F_gravity = m * g). The work done by gravity is given by the formula W_gravity = F_gravity * d * cos(theta), where d is the distance traveled and theta is the angle between the force and the direction of displacement.

2. Air Resistance: Air resistance is an opposing force that increases with velocity. As the skydiver accelerates, the air resistance also increases until it reaches a point where it is equal to the force of gravity. This is when the skydiver reaches terminal velocity, and the net force on her becomes zero, resulting in a constant velocity. At terminal velocity, the work done by air resistance is zero because the displacement of the skydiver is perpendicular to the force of air resistance, making the angle theta 90 degrees, and cos(90 degrees) = 0.

Now, let's consider each option and determine which one is correct:

A. The work done by gravity equals the negative of the work done by air resistance.
- This statement is not entirely true. While the work done by gravity and air resistance are related, they do not necessarily equal each other, especially when the skydiver reaches terminal velocity.

B. The work done by gravity is zero.
- This is not accurate since the skydiver is still subject to the force of gravity during the fall.

C. The work done by gravity equals the work done by air resistance.
- This is also incorrect. As mentioned earlier, the work done by air resistance at terminal velocity is zero, while the work done by gravity is not zero.

D. The work done by air resistance is 0.
- This is true. At terminal velocity, as explained before, the net force on the skydiver is zero, and hence the work done by air resistance is zero.

E. Her kinetic energy increases.
- This is not true. The work-energy theorem states that the work done on an object is equal to the change in its kinetic energy. Since the work done by air resistance is zero, the change in kinetic energy over that time interval is also zero. Therefore, her kinetic energy remains constant.

Considering the above analysis, the correct answer is D. The work done by air resistance is 0.