Maximum height of body thrown at angle to horizon

The maximum height of a projectile above its launch position is a function of the vertical component of the initial velocity, the angle between the initial velocity and the horizon, and the magnitude of the free fall acceleration.

Notation:

  1. \(g\) (g) is acceleration_due_to_gravity.

Conditions:

  1. \(\mathbf{v}_0 \cdot \mathbf{g} < 0\), i.e. the vector of initial velocity \(\mathbf{v}_0\) must have a non-zero component that is antiparallel to the vector of free fall acceleration \(\mathbf{g}\).

  2. The height is measured with respect to the horizontal plane where the projectile was located at initial time.

Links:

  1. Physics LibreTexts. Projectile Motion, Maximum Height (3.3.14).

height

Maximum height of the projectile.

Symbol:

h

Latex:

\(h\)

Dimension:

length

initial_speed

Initial speed of the body.

Symbol:

v_0

Latex:

\(v_{0}\)

Dimension:

velocity

angle

angle between the initial velocity and the horizon.

Symbol:

phi

Latex:

\(\varphi\)

Dimension:

angle

law

h = v_0^2 * sin(phi)^2 / (2 * g)

Latex:
\[h = \frac{v_{0}^{2} \sin^{2}{\left(\varphi \right)}}{2 g}\]