The Governing Equation
A falling parachutist experiences gravity pulling down and drag pushing up. The balance gives us this differential equation:
dv/dt = g − (c/m) × v
As velocity increases, drag increases too. Eventually they balance: acceleration becomes zero and velocity reaches terminal velocity.
Simulation
Real-time Values
Time
0.0 s
Velocity
0.0 m/s
Terminal velocity (analytical)
53.4 m/s
The Python Code You'll Write
This simulation runs the same loop you'll implement. Here's the core of Euler's method:
# Parameters from the textbook
m = 68.1 # mass in kg
c = 12.5 # drag coefficient in kg/s
g = 9.8 # gravitational acceleration in m/s²
dt = 0.5 # time step in seconds
# Initial conditions
v = 0 # starting velocity
t = 0 # starting time
# Euler's method loop
while t < 20:
# Calculate the slope (acceleration)
dvdt = g - (c/m) * v
# Update velocity: v_new = v_old + slope × Δt
v = v + dvdt * dt
t = t + dt
print(f"t = {t:.1f}s, v = {v:.2f} m/s")
Try changing the sliders above, then compare what you see to running this code yourself!