Time of flight of a projectile via maximum height
=================================================

Let the body be thrown horizontally with some initial velocity. Then the time of the motion
of this body until it reaches the initial elevation depends only on the height and acceleration
of free fall.

**Conditions:**

#. The acceleration of gravity stays constant throughout the movement of the body.

#. The initial and final height of the body with respect to the "ground" are the same,
   i.e. the body lands on a point with the same vertical coordinate as at the start
   of the flight.

**Links:**

#. `Physics LibreTexts. Zero Launch Angle, Duration of Flight (3.3.22) <https://phys.libretexts.org/Bookshelves/University_Physics/Physics_(Boundless)/3%3A_Two-Dimensional_Kinematics/3.3%3A_Projectile_Motion>`__.

..
    TODO rename file

.. py:currentmodule:: symplyphysics.laws.gravity.maximum_movement_time_of_a_body_thrown_horizontally

.. py:data:: time

    :attr:`~symplyphysics.symbols.basic.time` of flight of the projectile.

Symbol:
    :code:`t`

Latex:
    :math:`t`

Dimension:
    :code:`time`


.. py:data:: height

    Maximum :attr:`~symplyphysics.symbols.classical_mechanics.height` which the projectile reaches during its motion.

Symbol:
    :code:`h`

Latex:
    :math:`h`

Dimension:
    :code:`length`


.. py:data:: law

    :code:`t = sqrt(2 * h / g)`


    Latex:
        .. math::
            t = \sqrt{\frac{2 h}{g}}