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. \(\vec v_0 \cdot \vec g < 0\), i.e. the vector of initial velocity \(\vec v_0\) must have a non-zero component that is antiparallel to the vector of free fall acceleration \(\vec g\).

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:

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