Unit 3 - Problem 1 => Feather Terminal Velocity

Given:

$$weight_of_feather = .001kg$$ $$feather_air_resistance = b * V^2$$ $$b = .04$$

Reasoning:

$$F_{down} = m * a = .001kg * 10\frac{m}{s^2} = .01{Newtons}$$ $$F_{up} = b * V^2 = .04V^2$$ When these two force are equal, there is no further force and the V at that point is the terminal velocity. $${(F_{up} = b * V^2 = .04V^2)} = {(F_{down} = m * a = .001kg * 10\frac{m}{s^2} = .01{Newtons})}$$

Solving:

$$.04V^2 = .01{Newtons}$$ $$V^2 = \frac{.01}{.04} = \frac{1}{4}$$ $$V = \frac{1}{2} = 0.5\frac{m}{s^2}$$