Our task is to model the velocity profile of his descent. To start this problem assume the following: A parachutist with a mass $m = 80 \text{ kg}$, a cross-sectional area $S = 0.65 \text{ m}^2$, a drag coefficient $C_D = 0.45$ at an atmospheric density at sea level $\rho = 1.225 \frac{\text{kg}}{\text{m}^3}$ has an initial velocity of $v = 0 \frac{\text{m}}{\text{s}}$ after dropping out of a balloon. Numerically solve the equation below, plot the velocity-time relationship, and determine the terminal velocity. Also, discuss the formula with your peers. Can you find the terminal velocity analytically?
Differential equation:
$m \dot{V} = m \cdot g - \frac{\rho}{2} V^2 \cdot S \cdot C_D$
