Final answer:
The terminal velocity of an 80.0-kg skydiver falling in a headfirst position with a surface area of 0.140 m² is approximately 42.9 m/s (154 km/h).
Step-by-step explanation:
To find the terminal velocity of a skydiver falling in a headfirst position, we need to consider the weight of the skydiver and the area they present to the fluid. The formula to calculate terminal velocity is V = sqrt((2 * m * g) / (p * A * C)), where V is the terminal velocity, m is the mass of the skydiver, g is the acceleration due to gravity, p is the density of air, A is the surface area of the skydiver, and C is the drag coefficient. Assuming a drag coefficient of 1 for a skydiver in a headfirst position, we can calculate the terminal velocity.
Using the given values, the terminal velocity of the skydiver can be calculated as:
V = sqrt((2 * 80.0 * 9.8) / (1.2 * 0.140))
V ≈ 42.9 m/s
Converting this to kilometers per hour, we have:
V = 42.9 * 3.6 ≈ 154 km/h
Therefore, the correct option is b) 42.9 m/s (154 km/h).