import numpy as np import matplotlib.pyplot as plt class ProjectileSimulation: def __init__( self, g=9.81, C_d=0.01, v_init=100, theta=np.radians(180), h_init=10, dt=0.01, t_end=10, ): self.g = g self.C_d = C_d self.v_init = v_init self.theta = theta self.h_init = h_init self.dt = dt self.t_end = t_end self.reset() def reset(self): self.x = [0] self.y = [self.h_init] self.vx = [self.v_init * np.cos(self.theta)] self.vy = [self.v_init * np.sin(self.theta)] self.t = [0] def calculate_acceleration(self, t, state): x, y, vx, vy = state v = np.sqrt(vx**2 + vy**2) F_air_x = -self.C_d * v * vx F_air_y = -self.C_d * v * vy ax = F_air_x ay = F_air_y - self.g return [vx, vy, ax, ay] def update_state(self, t, state): k1 = self.calculate_acceleration(t, state) k2 = self.calculate_acceleration( t + 0.5 * self.dt, [s + 0.5 * self.dt * k for s, k in zip(state, k1)] ) k3 = self.calculate_acceleration( t + 0.5 * self.dt, [s + 0.5 * self.dt * k for s, k in zip(state, k2)] ) k4 = self.calculate_acceleration( t + self.dt, [s + self.dt * k for s, k in zip(state, k3)] ) return [ s + self.dt / 6 * (k1_i + 2 * k2_i + 2 * k3_i + k4_i) for s, k1_i, k2_i, k3_i, k4_i in zip(state, k1, k2, k3, k4) ] def run(self): while self.t[-1] < self.t_end: state = [self.x[-1], self.y[-1], self.vx[-1], self.vy[-1]] state = self.update_state(self.t[-1], state) self.x.append(state[0]) self.y.append(state[1]) self.vx.append(state[2]) self.vy.append(state[3]) self.t.append(self.t[-1] + self.dt) def plot(self): plt.plot(self.x, self.y) plt.xlabel("Horizontal distance (m)") plt.ylabel("Vertical distance (m)") plt.title("Projectile Motion with Air Resistance") plt.show() def print_range(self): range_projectile = self.x[-1] print(f"Range of projectile: {range_projectile:.2f} m")