We can use the equations of motion and the concept of terminal velocity to solve this problem.
Let's start by finding the terminal velocity:
A. Terminal Velocity:
The terminal velocity is the maximum velocity that a falling object can reach when the resistance of the medium through which it is falling (such as air) is equal to the force of gravity acting on the object. At terminal velocity, the net force on the object is zero, so the object moves at a constant velocity.
We can find the terminal velocity using the equation:
vT = mg/k
where vT is the terminal velocity, m is the mass of the object, g is the acceleration due to gravity, and k is the constant of proportionality.
Given that the body has a weight of 200 N, its mass is:
m = F/g = 200 N/9.81 m/s^2 ≈ 20.38 kg
We are also given that the constant of proportionality is k = 5 kg/s.
Therefore, the terminal velocity is:
vT = mg/k = (20.38 kg)(9.81 m/s^2)/5 kg/s ≈ 39.77 m/s
B. Height Traveled:
Next, we can use the equations of motion to find the height that the body traveled before reaching terminal velocity. At the maximum velocity, the net force on the body is zero, so the body moves at a constant velocity. We can use the equation:
v^2 = u^2 + 2as
where v is the final velocity (terminal velocity), u is the initial velocity (which is zero), a is the acceleration, and s is the distance traveled.
We can rearrange this equation to solve for s:
s = (v^2 - u^2)/2a = v^2/2a
At terminal velocity, the acceleration is zero, so we can use the terminal velocity we found in part (A) to find the height traveled:
s = vT^2/2a = (39.77 m/s)^2/(2 × 0) = 794.60 m
Therefore, the height that the body traveled before reaching terminal velocity is approximately 794.60 meters.