Maximum height from initial speed
=================================

The maximum height that a body thrown vertically will rise to depends on the initial speed.

**Notes:**

#. If the body is launched at an arbitrary angle to the horizontal, this formula is still
   applicable but you must use the projection of the velocity vector on the :math:`z` axis as the
   initial speed.

**Conditions:**

#. The body is thrown "upwards", i.e. in the direction opposite to that of the free fall
   acceleration vector.

**Links:**

#. `Wikipedia, fifth formula <https://en.wikipedia.org/wiki/Projectile_motion#Maximum_height_of_projectile>`__.

..
    TODO: move to kinetimatics

.. py:currentmodule:: symplyphysics.classical_mechanics.kinematics.projectile_motion.maximum_height_from_initial_speed

.. py:data:: maximum_height

    The maximum :attr:`~symplyphysics.symbols.classical_mechanics.height` that the object will reach.

Symbol:
    :code:`h`

Latex:
    :math:`h`

Dimension:
    :code:`length`


.. py:data:: initial_speed

    The initial :attr:`~symplyphysics.symbols.classical_mechanics.speed` of the object. Note that it is the *projection* of the body's velocity
    vector on the :math:`z`-axis.

Symbol:
    :code:`v`

Latex:
    :math:`v`

Dimension:
    :code:`velocity`


.. py:data:: law

    :code:`h = v^2 / (2 * g)`


    Latex:
        .. math::
            h = \frac{v^{2}}{2 g}