Tutorial_01_starter_code.py

import numpy as np
import matplotlib.pyplot as plt
from bisection import *
from dist import *

# Define a function witha root where the horizontal distanc equals R.
def F(theta):
    return

v0=
c=
g=
R = 
eps_x =    # The maximal error is stated in the assignment!
eps_f = 
kMax = 
# First task: solution(s) for R=85.0 (m).
theta, ... = bisect( ... )
if conv:
    print("First solution: R=%f, theta=%f +/- %f." % (R,theta,err))
else:
    print("Bisection did not converge!")
theta, ... = bisect( ... )
if conv:
    print("Second solution: R=%f, theta=%f +/- %f." % (R,theta,err))
else:
    print("Bisection did not converge!")

# Second task: find solutions in a range of values for R and plot the solution vs. R.
# First, let us get an impression of the maximal value of R:
angles = np.linspace(0,np.pi/2,100)
dists = dist(angles,c,g,v0)
plt.plot(angles,dists,'-*')
plt.xlabel('angle')
plt.ylabel('distance travelled')
plt.show()
# It seems the maximal reach is about 201(m). Let's try to automatically find the angles:
RMax =   
nPoints =   # Compute nPoints solutions on each "branch" (low and fast vs. high and looping).
split =     # By the eye, this is the angle that separates the branches.
Rs = np.linspace(0,RMax,nPoints)
# Complete two loops, one for each branch. For the first run, the initial interval is [0,split],
# for the second it is [split,pi/2].
result = [[0,0]]
for i in range(1,nPoints):
    R = Rs[i] # Note, that R is a global variable in this script.
    theta, ... = bisect( ... )
    if conv:
        result.append([R,theta])
    else:
        print("Bisection did not converge for R=%f." % (R))
for i in range(nPoints-1,0,-1):
    R = Rs[i]
    theta, ... = bisect( ... )
    if conv:
        result.append([R,theta])
    else:
        print("Bisection did not converge for R=%f." % (R))
result = np.array(result)
plt.plot(result[:,0],result[:,1],'-*')
plt.show()
# As you can see, there is an issue near the maximal value of R. Can you explain why?