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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

# Acceleration Constant on Earth (unit m/s^2)

g = 9.80665

def check_args(init_velocity: float, angle: float) -> None:

"""

Check that the arguments are valid

"""

# Ensure valid instance

if not isinstance(init_velocity, (int, float)):

raise TypeError("Invalid velocity. Should be a positive number.")

if not isinstance(angle, (int, float)):

raise TypeError("Invalid angle. Range is 1-90 degrees.")

# Ensure valid angle

if angle > 90 or angle < 1:

raise ValueError("Invalid angle. Range is 1-90 degrees.")

# Ensure valid velocity

if init_velocity < 0:

raise ValueError("Invalid velocity. Should be a positive number.")

def horizontal_distance(init_velocity: float, angle: float) -> float:

"""

Returns the horizontal distance that the object cover

Formula:

v_0^2 * sin(2 * alpha)

---------------------

v_0 - initial velocity

alpha - angle

>>> horizontal_distance(30, 45)

91.77

>>> horizontal_distance(100, 78)

414.76

>>> horizontal_distance(-1, 20)

Traceback (most recent call last):

...

ValueError: Invalid velocity. Should be a positive number.

>>> horizontal_distance(30, -20)

Traceback (most recent call last):

...

ValueError: Invalid angle. Range is 1-90 degrees.

"""

check_args(init_velocity, angle)

radians = angle_to_radians(2 * angle)

return round(init_velocity**2 * sin(radians) / g, 2)

def max_height(init_velocity: float, angle: float) -> float:

"""

Returns the maximum height that the object reach

Formula:

v_0^2 * sin^2(alpha)

--------------------

v_0 - initial velocity

alpha - angle

>>> max_height(30, 45)

22.94

>>> max_height(100, 78)

487.82

>>> max_height("a", 20)

Traceback (most recent call last):

...

TypeError: Invalid velocity. Should be a positive number.

>>> horizontal_distance(30, "b")

Traceback (most recent call last):

...

TypeError: Invalid angle. Range is 1-90 degrees.

"""

check_args(init_velocity, angle)

radians = angle_to_radians(angle)

return round(init_velocity**2 * sin(radians) ** 2 / (2 * g), 2)

def total_time(init_velocity: float, angle: float) -> float:

"""

Returns total time of the motion

Formula:

2 * v_0 * sin(alpha)

--------------------

v_0 - initial velocity

alpha - angle

>>> total_time(30, 45)

4.33

>>> total_time(100, 78)

19.95

>>> total_time(-10, 40)

Traceback (most recent call last):

...

ValueError: Invalid velocity. Should be a positive number.

>>> total_time(30, "b")

Traceback (most recent call last):

...

TypeError: Invalid angle. Range is 1-90 degrees.

"""

check_args(init_velocity, angle)

radians = angle_to_radians(angle)

return round(2 * init_velocity * sin(radians) / g, 2)

def test_motion() -> None:

"""

>>> test_motion()

"""

v0, angle = 25, 20

assert horizontal_distance(v0, angle) == 40.97

assert max_height(v0, angle) == 3.73

assert total_time(v0, angle) == 1.74

if __name__ == "__main__":

from doctest import testmod

testmod()

# Get input from user

init_vel = float(input("Initial Velocity: ").strip())

# Get input from user

angle = float(input("angle: ").strip())

# Print results

print()

print("Results: ")

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]")

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