import matplotlib.pyplot as plt
import numpy as np

g=9.8
v0=10
alpha=np.pi/4
N=100
tf=2.
tau=tf/N
h=0.

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=[h]

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,'r+',label='y(x)')
plt.legend()
plt.xlabel("x(m)")
plt.ylabel("y(m)")
plt.axis([0,12,0,3])
plt.title("trajectoire du boulet en chute libre")
plt.grid()
plt.show()