|
| 1 | +""" |
| 2 | +Horizontal Projectile Motion problem in physics. |
| 3 | +This algorithm solves a specific problem in which |
| 4 | +the motion starts from the ground as can be seen below: |
| 5 | + (v = 0) |
| 6 | + ** |
| 7 | + * * |
| 8 | + * * |
| 9 | + * * |
| 10 | + * * |
| 11 | + * * |
| 12 | +GROUND GROUND |
| 13 | +
|
| 14 | +For more info: https://en.wikipedia.org/wiki/Projectile_motion |
| 15 | +""" |
| 16 | + |
| 17 | +# Importing packages |
| 18 | +from math import pi, sin |
| 19 | + |
| 20 | +# Acceleration Constant on hearth (unit m/s^2) |
| 21 | +g = 9.80665 |
| 22 | + |
| 23 | + |
| 24 | +def angle_to_radians(angle): |
| 25 | + """ |
| 26 | + Convert an angle from degrees to randians |
| 27 | + """ |
| 28 | + return angle * pi / 180 |
| 29 | + |
| 30 | + |
| 31 | +def horizontal_distance(init_velocity: float, angle: float) -> float: |
| 32 | + """ |
| 33 | + Returns the horizontal distance that the object cover |
| 34 | +
|
| 35 | + Formula: |
| 36 | + v_0^2 * sin(2 * alpha) |
| 37 | + --------------------- |
| 38 | + g |
| 39 | +
|
| 40 | + v_0 - initial velocity |
| 41 | + alpha - angle |
| 42 | +
|
| 43 | + >>> horizontal_distance(30, 45) |
| 44 | + 91.77 |
| 45 | + >>> horizontal_distance(100, 78) |
| 46 | + 414.76 |
| 47 | + """ |
| 48 | + radians = angle_to_radians(2 * angle) |
| 49 | + return round((init_velocity ** 2) * sin(radians) / g, 2) |
| 50 | + |
| 51 | + |
| 52 | +def max_height(init_velocity: float, angle: float) -> float: |
| 53 | + """ |
| 54 | + Returns the maximum height that the object reach |
| 55 | +
|
| 56 | + Formula: |
| 57 | + v_0^2 * sin^2(alpha) |
| 58 | + -------------------- |
| 59 | + 2g |
| 60 | +
|
| 61 | + v_0 - initial velocity |
| 62 | + alpha - angle |
| 63 | +
|
| 64 | + >>> max_height(30, 45) |
| 65 | + 22.94 |
| 66 | + >>> max_height(100, 78) |
| 67 | + 487.82 |
| 68 | + """ |
| 69 | + |
| 70 | + radians = angle_to_radians(angle) |
| 71 | + return round(((init_velocity ** 2) * (sin(radians)) ** 2) / (2 * g), 2) |
| 72 | + |
| 73 | + |
| 74 | +def total_time(init_velocity: float, angle: float) -> float: |
| 75 | + """ |
| 76 | + Returns total time of the motion |
| 77 | +
|
| 78 | + Formula: |
| 79 | + 2 * v_0 * sin(alpha) |
| 80 | + -------------------- |
| 81 | + g |
| 82 | +
|
| 83 | + v_0 - initial velocity |
| 84 | + alpha - angle |
| 85 | +
|
| 86 | + >>> total_time(30, 45) |
| 87 | + 4.33 |
| 88 | + >>> total_time(100, 78) |
| 89 | + 19.95 |
| 90 | + """ |
| 91 | + |
| 92 | + radians = angle_to_radians(angle) |
| 93 | + return round((2 * init_velocity) * (sin(radians)) / g, 2) |
| 94 | + |
| 95 | + |
| 96 | +def test_motion() -> None: |
| 97 | + """ |
| 98 | + >>> test_motion() |
| 99 | + """ |
| 100 | + v0, angle = 25, 20 |
| 101 | + assert 40.97 == horizontal_distance(v0, angle) |
| 102 | + assert 3.73 == max_height(v0, angle) |
| 103 | + assert 1.74 == total_time(v0, angle) |
| 104 | + |
| 105 | + |
| 106 | +if __name__ == "__main__": |
| 107 | + |
| 108 | + # Get input from user |
| 109 | + init_vel = float(input("Initial Velocity: ")) |
| 110 | + |
| 111 | + # Get input from user |
| 112 | + angle = float(input("angle: ")) |
| 113 | + |
| 114 | + # Ensure valid angle |
| 115 | + if angle > 90 or angle <= 0: |
| 116 | + print("Error: Invalid angle. Range is 1-90 degrees.") |
| 117 | + |
| 118 | + # Ensure valid velocity |
| 119 | + elif init_vel < 0: |
| 120 | + print("Error: Invalid velocity. Should be a positive number.") |
| 121 | + |
| 122 | + # Print results |
| 123 | + else: |
| 124 | + print() |
| 125 | + h_dis = str(horizontal_distance(init_vel, angle)) |
| 126 | + v_dis = str(max_height(init_vel, angle)) |
| 127 | + t_time = str(total_time(init_vel, angle)) |
| 128 | + print("Results: ") |
| 129 | + print("Horizontal Distance: " + h_dis + " [m]") |
| 130 | + print("Maximum Height: " + v_dis + " [m]") |
| 131 | + print("Total Time: " + t_time + " [s]") |
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