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I have managed to write the following code for the following problem:

Projectile's horizontal and vertical displacement are given by:

$$ x = v_0 \, t \cos(\theta) $$

$$ y = v_0 \, t \sin(\theta) - \frac{1}{2}gt^2$$

  • Consider the time interval to be $t \in [0, 60] seconds$. Write a Python code to plot horizontal and maximum vertical displacements (meaning $y_{max.}$ as a function of $x$) with the initial velocity $40 m/sec$ for four angles (30, 45, 60, and 75 degrees ) on the same graph. Then save your data in a text file.

My code is:

import numpy as np
import matplotlib.pyplot as plt

v = 40
g = 9.8

def x(theta):
    return ((v*t)*np.cos(theta*np.pi/180))

def y(theta):
    return ((v*t)*np.sin(theta*np.pi/180))-((0.5*g)*(t**2))


for theta in range(30, 90, 15):
    tmax = v * np.sin(theta*np.pi/180)/g  #Time to reach maximum height
    t = np.linspace(0, tmax,600)
    
    X = x(theta)  #Maximum horizontal displacement at tmax
    Y = y(theta)  #Maximum vertical displacement at tmax
    
    plt.plot(X, Y, label=theta)
    
    table=np.column_stack((t,X, Y))                             
np.savetxt("projectile.txt", table, fmt='%.3e', delimiter="  ")  # just saves 3 columns :(


    
plt.xlabel("x")
plt.ylabel("y")
plt.title("Maximum Height as a Function of Angle")
plt.legend()
plt.show()

enter image description here

I get the plot successfully; however, the data saved consistes of 3 columns only, whereas it should be 9 columns.

How to save all the data please? Your help is much appreciated.

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Well, you "overwrite" the table at every loop... As a result when the for loop is terminated the table has only the t,X,Y columns for theta=75.

Try this:

columns = []

for theta in range(30, 90, 15):
    tmax = v * np.sin(theta*np.pi/180)/g  #Time to reach maximum height
    t = np.linspace(0, tmax,600)
    
    X = x(theta)  #Maximum horizontal displacement at tmax
    Y = y(theta)  #Maximum vertical displacement at tmax
    
    plt.plot(X, Y, label=theta)
    
    columns += [t,X,Y]
                          
np.savetxt("projectile.txt", np.column_stack(columns), fmt='%.3e', delimiter="  ")
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  • $\begingroup$ Very nice! But instead of 9 columns this saves 12 columns, I think there must be an error; I could not figure out the reason why instead of 9 columns there exists 12 columns. could you help me please? $\endgroup$ – Sha Feb 17 at 12:39
  • $\begingroup$ 3 columns(t,X,Y) * 4 theta cases(30,45,60,75) = 12. $\endgroup$ – Saranta Podarakis Feb 17 at 12:46
  • $\begingroup$ I understand now! and I can not thank you enough for your help. $\endgroup$ – Sha Feb 17 at 13:01
  • $\begingroup$ If you want to have only one column for the time, maybe it would be a good idea to change your impementation, so that there will be the same t for all angles. Otherwise, the data that you will save will not make any sense... $\endgroup$ – Saranta Podarakis Feb 17 at 13:23
  • $\begingroup$ Yes that would be nice to have only one column for the time, but that is not possible in our case, because the time interval is itself a function of the angle. With each theta case the $tmax.$ changes, which in turn changes the value of the 600 time coordinates within the np.linspace time interval. $\endgroup$ – Sha Feb 17 at 13:35

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