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

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:

$\phi$

Dimension:

angle

law

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

Latex:

$$h=\frac{v_0^2{\sin }^2\left(\phi \right)}{2g}$$