Question

use python to graph the projectile motion of an object under quadratic drag

Answer 1

As you have not specified the mass of the particle, the angle, it's inital velocity, angle of projection, etc., here is a general python program which you can use accordingly.

import numpy as np

import matplotlib.pyplot as plt

% matplotlib inline

# Model parameters

M = (put some value) # Mass of projectile in kg

g = 9.8 # Acceleration due to gravity (m/s^2)

V = () # Initial velocity in m/s

ang = () # Angle of initial velocity in degrees

Cd = () # Drag coefficient

dt = () # time step in s

t = [0]

vx = [V*np.cos(ang/180*np.pi)]

vy = [V*np.sin(ang/180*np.pi)]

x = [0]

y = [0]

drag=Cd*V**2

ax = [-(drag*np.cos(ang/180*np.pi))/M ]

ay = [-g-(drag*np.sin(ang/180*np.pi)/M) ]

counter = 0

while (y[counter] >= 0):

t.append(t[counter]+dt)

vx.append(vx[counter]+dt*ax[counter])

vy.append(vy[counter]+dt*ay[counter])

x.append(x[counter]+dt*vx[counter])

y.append(y[counter]+dt*vy[counter])

vel = np.sqrt(vx[counter+1]**2 + vy[counter+1]**2)

drag = Cd*vel**2

ax.append(-(drag*np.cos(ang/180*np.pi))/M)

ay.append(-g-(drag*np.sin(ang/180*np.pi)/M))

counter = counter +1

plt.plot(x,y,'ro')

plt.ylabel("y (m)")

plt.xlabel("x (m)")

print "Range of projectile is {:3.1f} m".format(x[counter])