fasttrajectory

10@njit
11def simulate_projectile(
12    velocity: float,
13    angle_deg: float,
14    dt: float = 0.01,
15    drag: float = 0.0,
16    gravity: float = 9.81,
17):
18    """
19    Simulate projectile motion with optional air drag.
20
21    Parameters
22    ----------
23    velocity : float
24        Initial velocity in m/s.
25    angle_deg : float
26        Launch angle in degrees.
27    dt : float
28        Time step in seconds.
29    drag : float
30        Air resistance coefficient.
31    gravity : float
32        Gravitational acceleration in m/s^2.
33
34    Returns
35    -------
36    tuple[np.ndarray, np.ndarray]
37        Arrays of x and y coordinates.
38    """
39
40    angle_rad = np.radians(angle_deg)
41
42    vx = velocity * np.cos(angle_rad)
43    vy = velocity * np.sin(angle_rad)
44
45    x = 0.0
46    y = 0.0
47
48    xs = [x]
49    ys = [y]
50
51    while y >= 0:
52
53        speed = np.sqrt(vx**2 + vy**2)
54
55        ax = -drag * speed * vx
56        ay = -gravity - drag * speed * vy
57
58        vx += ax * dt
59        vy += ay * dt
60
61        x += vx * dt
62        y += vy * dt
63
64        xs.append(x)
65        ys.append(y)
66
67    return np.array(xs), np.array(ys)

71def flight_time(
72    velocity: float,
73    angle_deg: float,
74    gravity: float = 9.81,
75) -> float:
76    """
77    Compute total projectile flight time without air resistance.
78
79    Parameters
80    ----------
81    velocity : float
82        Initial velocity in m/s.
83
84    angle_deg : float
85        Launch angle in degrees.
86
87    gravity : float
88        Gravitational acceleration in m/s^2.
89
90    Returns
91    -------
92    float
93        Total flight time in seconds.
94    """
95    angle_rad = np.radians(angle_deg)
96
97    return 2 * velocity * np.sin(angle_rad) / gravity