Final answer:
The terminal velocity of a person falling in air depends on their weight and the area facing the fluid. For an 80.0-kg skydiver with a surface area of 0.140 m², the terminal velocity can be calculated by balancing the drag force with the gravitational force.
Step-by-step explanation:
The terminal velocity of a person falling in air is determined by both the weight of the person and the area of the person facing the fluid. When a skydiver reaches terminal velocity, the force of air drag equals the gravitational force, leading to a net force of zero and no further acceleration. The drag force in turbulent conditions for a person with a high speed and large body size is approximately proportional to the square of the velocity (FD = pAv²).
Calculation of Terminal Velocity
To find the terminal velocity of an 80.0-kg skydiver falling in a headfirst position with a surface area of 0.140 m², you use the balance between the drag force and the weight of the skydiver. The formula FD = mg can be rearranged to solve for the terminal velocity (vt). By inputting the appropriate values for mass (m), gravitational acceleration (g), density of air (p), and cross-sectional area (A), along with the drag coefficient (C), you can calculate the terminal speed in meters per second and then convert it to kilometers per hour.