def newton(v, alpha):
    if alpha <= 0 or alpha >= pi/2:
        print("Bad angle")
        return .0
    
    def fx(t, v):
        return -(beta*v**2)
    
    def fy(t, v):
        return -copysign(1, v)*beta*v**2-g
    
    dvx, dvy = RK4(fx), RK4(fy)
    dt = 0.0001 
    vx, vy = v*cos(alpha), v*sin(alpha)
    t = dt
    x_old = y_old = 0
    x = vx*dt
    y = vy*dt
    
    while (y > 0):
        t += dt
        vx_new = vx + dvx(t, vx, dt)
        vy_new = vy + dvy(t, vy, dt)
        x_old = x
        x += (vx_new + vx) * dt / 2
        y_old = y
        y += (vy_new + vy) * dt / 2
        vx = vx_new
        vy = vy_new
    
    if y_old == 0:
        return x_old
    return (x_old*(y_old - y) - y_old*(x_old-x))/(y_old - y)