TheAlgorithms-Python/physics/horizontal_projectile_motion.py

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"""
Horizontal Projectile Motion problem in physics.
This algorithm solves a specific problem in which
the motion starts from the ground as can be seen below:
(v = 0)
**
* *
* *
* *
* *
* *
GROUND GROUND
For more info: https://en.wikipedia.org/wiki/Projectile_motion
"""
# Importing packages
from math import radians as angle_to_radians
from math import sin
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# Acceleration Constant on hearth (unit m/s^2)
g = 9.80665
def horizontal_distance(init_velocity: float, angle: float) -> float:
"""
Returns the horizontal distance that the object cover
Formula:
v_0^2 * sin(2 * alpha)
---------------------
g
v_0 - initial velocity
alpha - angle
>>> horizontal_distance(30, 45)
91.77
>>> horizontal_distance(100, 78)
414.76
"""
radians = angle_to_radians(2 * angle)
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return round(init_velocity ** 2 * sin(radians) / g, 2)
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def max_height(init_velocity: float, angle: float) -> float:
"""
Returns the maximum height that the object reach
Formula:
v_0^2 * sin^2(alpha)
--------------------
2g
v_0 - initial velocity
alpha - angle
>>> max_height(30, 45)
22.94
>>> max_height(100, 78)
487.82
"""
radians = angle_to_radians(angle)
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return round((init_velocity ** 2 * sin(radians) ** 2) / (2 * g), 2)
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def total_time(init_velocity: float, angle: float) -> float:
"""
Returns total time of the motion
Formula:
2 * v_0 * sin(alpha)
--------------------
g
v_0 - initial velocity
alpha - angle
>>> total_time(30, 45)
4.33
>>> total_time(100, 78)
19.95
"""
radians = angle_to_radians(angle)
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return round(2 * init_velocity * sin(radians) / g, 2)
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def test_motion() -> None:
"""
>>> test_motion()
"""
v0, angle = 25, 20
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assert horizontal_distance(v0, angle) == 40.97
assert max_height(v0, angle) == 3.73
assert total_time(v0, angle) == 1.74
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if __name__ == "__main__":
# Get input from user
init_vel = float(input("Initial Velocity: "))
# Get input from user
angle = float(input("angle: "))
# Ensure valid angle
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if angle > 90 or angle < 1:
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print("Error: Invalid angle. Range is 1-90 degrees.")
# Ensure valid velocity
elif init_vel < 0:
print("Error: Invalid velocity. Should be a positive number.")
# Print results
else:
print()
print("Results: ")
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print(f"Horizontal Distance: {str(horizontal_distance(init_vel, angle))} [m]")
print(f"Maximum Height: {str(max_height(init_vel, angle))} [m]")
print(f"Total Time: {str(total_time(init_vel, angle))} [s]")