Plots for https://lisakov.com/blog/growing-displacement/

r_t.py

import numpy as np

def cos(x):
    return round( np.cos( np.radians(x) ), 10 )
def sin(x):
    return round( np.sin( np.radians(x) ), 10 )
def asin(x):
    return np.degrees( np.arcsin(x) )

# Plot setup {{{
from matplotlib import pyplot as plt
from matplotlib import rc, rcParams
rcParams['font.size'] = 16.
rcParams['text.usetex'] = True
rcParams['font.sans-serif'] = ['Computer Modern']
rc('text.latex', preamble=r'\usepackage[T2A]{fontenc} \usepackage[utf8]{inputenc}')
rc('axes', linewidth=1.2)
rc('xtick.major', size=4, width=1.1)
rc('ytick.major', size=4, width=1.1)
fig, ax = plt.subplots()
fig.subplots_adjust(left=.15, bottom=.15, right=.95, top=.95)
#}}}

def sqrt(x): return x**(1./2.)

v = 20
g = 10
t = np.linspace(0,5,100)
angles = [0,20,40,50,60,asin(sqrt(8/9)),78,83,90]

for a in angles:
    x = v * cos(a) * t
    y = v * sin(a) * t - g*t**2 / 2
    r = sqrt(x**2 + y**2)

    ax.plot(t,r)

ax.grid()
ax.set_xlabel('$t$ [\\textrm{с}]')
ax.set_ylabel('$r$ [\\textrm{м}]')
ax.set_ylim([0,80])

#plt.savefig('r_t.png', bbox_inches='tight')

plt.show()

rv_a.py

import numpy as np

# Triginometry {{{
def cos(x):
    return round( np.cos( np.radians(x) ), 10 )
def sin(x):
    return round( np.sin( np.radians(x) ), 10 )
def sins(x):
    return round( np.sin( np.radians(x) )**2, 10 )
def asin(x):
    return np.degrees( np.arcsin(x) )
#}}}
def sqrt(x): return x**(1./2.)

# Plot setup {{{
from matplotlib import pyplot as plt
from matplotlib import rc, rcParams
rcParams['font.size'] = 16.
rcParams['text.usetex'] = True
rcParams['font.sans-serif'] = ['Computer Modern']
rc('text.latex', preamble=r'\usepackage[T2A]{fontenc} \usepackage[utf8]{inputenc} \usepackage{bm}')
rc('axes', linewidth=1.2)
rc('xtick.major', size=4, width=1.1)
rc('ytick.major', size=4, width=1.1)
fig, ax = plt.subplots()
fig.subplots_adjust(left=.15, bottom=.15, right=.95, top=.95)
#}}}

# Initial parameters (SI units)
x0 = 0
y0 = 0
v0 = 20
g  = 10

#a = asin(sqrt(8/9)) # 70.53 deg

t = np.linspace(0,5,100)

angles = np.linspace(90, 55, 300)

for a in angles:

    # Kinematics equations
    x = v0*cos(a)*t
    y = v0*sin(a)*t - g*t**2/2
    vx = v0*cos(a)
    vy = v0*sin(a) - g*t

    if a >= asin(sqrt(8/9)) and a < 88.3:
        # First time when r is perpendicular to v
        t1 = (3/2*v0*g*sin(a) - sqrt(9/4*v0**2*g**2*sins(a) - 2*g**2*v0**2)) / g**2
        x1  = v0*cos(a)*t1
        y1  = v0*sin(a)*t1 - g*t1**2/2
        v1y = v0*sin(a) - g*t1

        # Second time when r is perpendicular to v
        t2 = (3/2*v0*g*sin(a) + sqrt(9/4*v0**2*g**2*sins(a) - 2*g**2*v0**2)) / g**2
        x2  = v0*cos(a)*t2
        y2  = v0*sin(a)*t2 - g*t2**2/2
        v2y = v0*sin(a) - g*t2

        # v1
        ax.arrow(x1, y1, vx, v1y, 
            width=0.3, 
            head_length=1, 
            ec='None',
            fc='#FF5555',
            zorder=4,
            length_includes_head=True)
        ax.text((x1+vx)*1.06, y1+v1y, '$\\bm{v_1}$', c='#FF5555', ha='left')

        # v2
        ax.arrow(x2, y2, vx, v2y, 
            width=0.3, 
            head_length=1, 
            ec='None',
            fc='#FF5555',
            zorder=5,
            length_includes_head=True)
        ax.text((x2+vx)*1.05, y2+v2y, '$\\bm{v_2}$', c='#FF5555', ha='left')

        # r1
        ax.arrow(x0, y0, x1, y1, 
            width=0.3, 
            head_length=1.5, 
            ec='None',
            fc='#3333BB',
            length_includes_head=True)
        ax.text((x0+x1)/2.2 , (y0+y1)/2, '$\\bm{r_1}$', c='#3333BB', ha='right')

        # r2
        ax.arrow(x0, y0, x2, y2, 
            width=0.3, 
            head_length=1.5, 
            ec='None',
            fc='#3333BB',
            length_includes_head=True)
        ax.text((x0+x2)/1.95 , (y0+y2)/2, '$\\bm{r_2}$', c='#3333BB', ha='left', va='top')

    # Final plot setup and trajectory

    #ax.text(30.9, 16, '$\\alpha={}^\\circ$'.format(int(a)))
    ax.plot([], [], ' ', label='$v_0={}~$'.format(v0)+'\\textrm{м/с}')
    ax.plot([], [], ' ', label='$\\alpha={}^\circ$'.format( "{:.1f}".format(a)) )

    ax.legend(markerscale=0, handletextpad=-2.0)

    ax.grid()
    ax.plot(x, y, ls='-', c='#888888', lw=1.4)
    plt.axis('equal')
    ax.set_axisbelow(True)
    ax.set_xlim([-0,45])
    ax.set_ylim([-20,25])
    ax.set_xlabel('$x$ [\\textrm{м}]')
    ax.set_ylabel('$y$ [\\textrm{м}]')

    # Save the figure
    plt.savefig('rpvt_a/' + str(a)+'.png', bbox_inches='tight')
    plt.cla()

    # Use imagemagick to convert *.png to *.gif:
    # convert -delay 0.01 -loop 0 -reverse *.png r.gif

rv_t.py

import numpy as np

# Triginometry {{{
def cos(x):
    return round( np.cos( np.radians(x) ), 10 )
def sin(x):
    return round( np.sin( np.radians(x) ), 10 )
def sins(x):
    return round( np.sin( np.radians(x) )**2, 10 )
def asin(x):
    return np.degrees( np.arcsin(x) )
#}}}
def sqrt(x): return x**(1./2.)
# Plot setup {{{
from matplotlib import pyplot as plt
from matplotlib import rc, rcParams
rcParams['font.size'] = 16.
rcParams['text.usetex'] = True
rcParams['font.sans-serif'] = ['Computer Modern']
rc('text.latex', preamble=r'\usepackage[T2A]{fontenc} \usepackage[utf8]{inputenc} \usepackage{bm}')
rc('axes', linewidth=1.2)
rc('xtick.major', size=4, width=1.1)
rc('ytick.major', size=4, width=1.1)
fig, ax = plt.subplots()
fig.subplots_adjust(left=.15, bottom=.15, right=.95, top=.95)
#}}}

# Initial parameters (SI units)
x0 = 0
y0 = 0
v0 = 20
g  = 10
a  = 75


times = np.linspace(0.001, 4.5, 200)
rs=[]
drs=[]
cmap = plt.get_cmap('coolwarm')
cmapb = plt.get_cmap('Blues')
cmapr = plt.get_cmap('Oranges')

i=0
for t in times:
    x = v0*cos(a)*t
    y = v0*sin(a)*t - g*t**2/2
    r = sqrt(x**2+y**2)
    rs = np.append(rs, r)
    drs = np.append(drs, rs[i]-rs[i-1])
    i+=1

drs /= np.amax(drs)

i=0
for t in times:

    # Kinematics equations
    x = v0*cos(a)*t
    y = v0*sin(a)*t - g*t**2/2
    vx = v0*cos(a)
    vy = v0*sin(a) - g*t

    # v
    vc = '#333333'
    ax.arrow(x, y, vx, vy, 
        width=0.3, 
        head_length=1, 
        ec='None',
        fc=vc,
        zorder=4,
        length_includes_head=True)
    ax.text((x+vx)*1.03, y+vy, '$\\bm{v}$', c=vc, ha='left')

    # r
    if drs[i]>=0:
        fcr=cmapb(10+int(drs[i]*400))
    else:
        fcr=cmapr(10+int(abs(drs[i])*600))
    print (int(drs[i]*256))
    ax.arrow(x0, y0, x, y, 
        width=0.3, 
        head_length=1.5, 
        ec='None',
        fc=fcr,
        length_includes_head=True)
    ax.text((x0+x)/2 , (y0+y)/2 - 1, '$\\bm{r}$', c=fcr, ha='center', va='top')

    # Final plot setup and trajectory
    times = np.linspace(0,5,100)
    x = v0*cos(a)*times
    y = v0*sin(a)*times - g*times**2/2
    vx = v0*cos(a)
    vy = v0*sin(a) - g*times
    ax.plot(x, y, ls='-', c='#888888', lw=1.4)

    ax.plot([], [], ' ', label='$v_0={}~$'.format(v0)+'\\textrm{м/с}')
    ax.plot([], [], ' ', label='$\\alpha={}^\circ$'.format(a))
    ax.plot([], [], ' ', label='$t={}~$'.format( "{:.1f}".format(t) )+'\\textrm{с}')

    ax.legend(markerscale=0, handletextpad=-2.0)

    ax.grid()
    plt.axis('equal')
    ax.set_axisbelow(True)
    ax.set_xlim([-10,80])
    ax.set_ylim([-55,40])
    ax.set_xlabel('$x$ [\\textrm{м}]')
    ax.set_ylabel('$y$ [\\textrm{м}]')

    # Save the figure
    plt.savefig('rv_t/' + str(a) + '_' + str(t)+'.png', bbox_inches='tight')
    plt.cla()
    i+=1

# Use imagemagick to convert *.png to *.gif:
# convert -delay 0.01 -loop 0 -reverse *.png r.gif