import numpy as np
import matplotlib.pyplot as plt
% matplotlib inline

# Model parameters
M = 0.008          # Mass of projectile in kg
g = 9.8          # Acceleration due to gravity (m/s^2)
V = 0           # Initial velocity in m/s
ang = 90.0       # Angle of initial velocity in degrees
Cd = 0.005       # Drag coefficient
dt = 0.5         # time step in s

# You can check the variables by printing them out
print V, ang

# Set up the lists to store variables
# Initialize the velocity and position at t=0
t = [0]                         # list to keep track of time
vx = [V*np.cos(ang/180*np.pi)]  # list for velocity x and y components
vy = [V*np.sin(ang/180*np.pi)]
x = [0]                         # list for x and y position
y = [0.3]

# Drag force
drag = Cd*V**2                      # drag force 

# Acceleration components
ax = [-drag*np.cos(ang/180*np.pi)/M]          
ay = [-g-drag*np.sin(ang/180*np.pi)/M]

## Leave this out for students to try
# We can choose to have better control of the time-step here
dt = 0.001

# Use Euler method to update variables
counter = 0
while (y[counter] >= 0):                   # Check that the last value of y is >= 0
    t.append(t[counter]+dt)                # increment by dt and add to the list of time 
    
    
    
    # Update velocity
    vx.append(vx[counter]+dt*ax[counter])  
    vy.append(vy[counter]+dt*ay[counter])

    # Update position
    x.append(x[counter]+dt*vx[counter])    
    y.append(y[counter]+dt*vy[counter])    

    # With the new velocity calculate the drag force and update acceleration
    vel = np.sqrt(vx[counter+1]**2 + vy[counter+1]**2)                   # magnitude of velocity
    drag = Cd*vel**2                  # drag force 
    ax.append(-drag*(vx[counter+1]/vel)/M)
    ay.append(-g-drag*(vy[counter+1]/vel)/M)
    
    # Increment the counter by 1
    counter = counter +1

# Let's plot the trajectory
plt.plot(t,y,'ro')
plt.ylabel("y (m)")
plt.xlabel("t (s)")
   
# The last value of x should give the range of the projectile approximately.

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

0 90.0
Range of projectile is 0.0 m

y1 = y
t1 = t
plt.plot(t1,y1,'ro')

[<matplotlib.lines.Line2D at 0x7fa7502ab350>]

import numpy as np
import matplotlib.pyplot as plt
% matplotlib inline

# Model parameters
M = 0.008          # Mass of projectile in kg
g = 9.8          # Acceleration due to gravity (m/s^2)
V = 0           # Initial velocity in m/s
ang = 90.0       # Angle of initial velocity in degrees
Cd = 0.1       # Drag coefficient
dt = 0.5         # time step in s

# You can check the variables by printing them out
print V, ang

# Set up the lists to store variables
# Initialize the velocity and position at t=0
t = [0]                         # list to keep track of time
vx = [V*np.cos(ang/180*np.pi)]  # list for velocity x and y components
vy = [V*np.sin(ang/180*np.pi)]
x = [0]                         # list for x and y position
y = [0.3]

# Drag force
drag = Cd*V**2                      # drag force 

# Acceleration components
ax = [-drag*np.cos(ang/180*np.pi)/M]          
ay = [-g-drag*np.sin(ang/180*np.pi)/M]

## Leave this out for students to try
# We can choose to have better control of the time-step here
dt = 0.001

# Use Euler method to update variables
counter = 0
while (y[counter] >= 0):                   # Check that the last value of y is >= 0
    t.append(t[counter]+dt)                # increment by dt and add to the list of time 
    
    
    
    # Update velocity
    vx.append(vx[counter]+dt*ax[counter])  
    vy.append(vy[counter]+dt*ay[counter])

    # Update position
    x.append(x[counter]+dt*vx[counter])    
    y.append(y[counter]+dt*vy[counter])    

    # With the new velocity calculate the drag force and update acceleration
    vel = np.sqrt(vx[counter+1]**2 + vy[counter+1]**2)                   # magnitude of velocity
    drag = Cd*vel**2                  # drag force 
    ax.append(-drag*(vx[counter+1]/vel)/M)
    ay.append(-g-drag*(vy[counter+1]/vel)/M)
    
    # Increment the counter by 1
    counter = counter +1

# Let's plot the trajectory
plt.plot(t,y,'ro')
plt.ylabel("y (m)")
plt.xlabel("t (s)")
   
# The last value of x should give the range of the projectile approximately.

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

0 90.0
Range of projectile is 0.0 m

y2 = y
t2 = t
plt.plot(t2,y2,'ro')
plt.plot(t1,y1,'ro')

[<matplotlib.lines.Line2D at 0x7fa75031da50>]

import numpy as np
import matplotlib.pyplot as plt
% matplotlib inline

# Model parameters
M = 0.008          # Mass of projectile in kg
g = 9.8          # Acceleration due to gravity (m/s^2)
V = 0           # Initial velocity in m/s
ang = 90.0       # Angle of initial velocity in degrees
Cd = 0.15       # Drag coefficient
dt = 0.5         # time step in s

# You can check the variables by printing them out
print V, ang

# Set up the lists to store variables
# Initialize the velocity and position at t=0
t = [0]                         # list to keep track of time
vx = [V*np.cos(ang/180*np.pi)]  # list for velocity x and y components
vy = [V*np.sin(ang/180*np.pi)]
x = [0]                         # list for x and y position
y = [0.3]

# Drag force
drag = Cd*V**2                      # drag force 

# Acceleration components
ax = [-drag*np.cos(ang/180*np.pi)/M]          
ay = [-g-drag*np.sin(ang/180*np.pi)/M]

## Leave this out for students to try
# We can choose to have better control of the time-step here
dt = 0.001

# Use Euler method to update variables
counter = 0
while (y[counter] >= 0):                   # Check that the last value of y is >= 0
    t.append(t[counter]+dt)                # increment by dt and add to the list of time 
    
    
    
    # Update velocity
    vx.append(vx[counter]+dt*ax[counter])  
    vy.append(vy[counter]+dt*ay[counter])

    # Update position
    x.append(x[counter]+dt*vx[counter])    
    y.append(y[counter]+dt*vy[counter])    

    # With the new velocity calculate the drag force and update acceleration
    vel = np.sqrt(vx[counter+1]**2 + vy[counter+1]**2)                   # magnitude of velocity
    drag = Cd*vel**2                  # drag force 
    ax.append(-drag*(vx[counter+1]/vel)/M)
    ay.append(-g-drag*(vy[counter+1]/vel)/M)
    
    # Increment the counter by 1
    counter = counter +1

# Let's plot the trajectory
plt.plot(t,y,'ro')
plt.ylabel("y (m)")
plt.xlabel("t (s)")
   
# The last value of x should give the range of the projectile approximately.

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

0 90.0
Range of projectile is 0.0 m

y3 = y
t3 = t
plt.plot(t2,y2,'ro')
plt.plot(t1,y1,'ro')
plt.plot(t3,y3,'ro')

[<matplotlib.lines.Line2D at 0x7fa750225b50>]