import matplotlib.pyplot as plt
import numpy as np

g=9.8
v0=10
N=100
tf=3.
tau=tf/N
Nbis=20

for j in range(Nbis):
    alpha=np.pi/2*j/Nbis
    ax=[0 for i in range(N)]
    ay=[-g for i in range(N)]
    vx=[v0*np.cos(alpha) for i in range(N)]
    vy=[v0*np.sin(alpha)]
    x=[0]
    y=[0]
    t=[tau*i for i in range(N)]
    for i in range(N-1):
        vy.append(vy[i]+ay[i]*tau)
    for i in range(N-1):
        x.append(x[i]+vx[i]*tau)
        y.append(y[i]+vy[i]*tau)
    plt.plot(x,y)
    plt.axis([0,15,0,10])
    plt.xlabel("x(m)")
    plt.ylabel("y(m)")
    plt.grid()
    plt.show()