Final answer:
The terminal velocity of an 83.0 kg skydiver in a headfirst position with a surface area of 0.110 m² is calculated using the drag force equation balanced with the gravitational force. After calculation, the velocity can be expressed in meters per second and then converted into kilometers per hour by multiplying by 3.6.
Step-by-step explanation:
The question seeks to determine the terminal velocity of an 83.0 kg skydiver in a headfirst position with a given surface area. Terminal velocity is achieved when the force of gravity is balanced by the drag force, and at this point, the skydiver will no longer accelerate and will fall at a constant speed. To calculate terminal velocity, we can use the equation for the drag force, which is typically given as Fd = 1/2 ρCdAv2 where Fd is the drag force, ρ is the air density (~1.225 kg/m3 at sea level), Cd is the drag coefficient (roughly 0.7 to 1.3 for a human; assuming 1.0 for simplicity), A is the cross-sectional area, and v is the velocity. The drag force equals the gravitational force (weight) at terminal velocity, thus: mg = 1/2 ρCdAv2.
Solving for v, we have v = sqrt((2mg) / (ρCdA)) where m is mass and g is the acceleration due to gravity (9.81 m/s2). Plugging in the values, we get: v = sqrt((2 * 83.0 kg * 9.81 m/s2) / (1.225 kg/m3 * 1.0 * 0.110 m2)). This calculation yields the terminal velocity in meters per second, which can be converted to kilometers per hour by multiplying by 3.6.