Main Answer
The air friction coefficient for this scenario is cw = 0.70, and the frontal surface area of the person is A = 0.60 m². To estimate the mass, we can use the formula for terminal velocity (v) in still air:v = -(cw) (ρ) (A) (v)² / (2 (m)).Here, ρ is the density of air. Since we know cw, A, and v is not yet known, we can solve for m:m = -(cw) (ρ) (A) (v)² / (2 (v)).
We don't know v yet, but we can make an educated guess based on the fact that a falling human body reaches a terminal velocity of around 54 m/s (200 km/h). Using this value, we can estimate the mass:m = -(0.70) (1.2 kg/m³) (0.60 m²) (54 m/s)² / (2 (54 m/s))m ≈ 0.42 kgThe option C is correct.
Explanation:
To understand why we're using this formula and what it means, let's break it down. The formula for terminal velocity in still air is derived from Newton's second law of motion, which states that force equals mass times acceleration.
In this case, the force acting on the falling body is the drag force from the air. This force is proportional to the square of the velocity, which means that as the body falls faster, it encounters more resistance from the air.
This resistance slows down the body until it reaches a constant velocity called terminal velocity. The formula above takes into account this relationship between velocity and drag force to calculate the mass required to achieve a certain terminal velocity.
The value of cw is a dimensionless coefficient that represents the drag force per unit frontal area. It depends on various factors such as body shape, orientation, and speed.
In this scenario, we're assuming a value of 0.70 for cw, which is typical for a human body in a standing position with arms and legs slightly spread out.
The frontal surface area A is also important because it determines how much air the body interacts with at any given time. In this case, we're assuming a value of 0.60 m² for A, which is roughly equivalent to the frontal area of an average adult human.
By combining these values with the density of air and some basic algebraic manipulation, we can estimate the mass required to achieve a certain terminal velocity in still air. This calculation assumes that there are no other external forces acting on the body besides gravity and drag force from the air.
In reality, there may be other factors such as wind resistance or friction with surfaces that could affect the terminal velocity and mass calculation. However, for our purposes here, we're simplifying things to illustrate how these variables interact with each other in this context.The option C is correct.