Formula: Horizontal throw Throw distance Initial speed Initial height
$$w ~=~ v_0 \, \sqrt{ \frac{2\, y_0}{ g } }$$
$$w ~=~ v_0 \, \sqrt{ \frac{2\, y_0}{ g } }$$
$$v_0 ~=~ w \, \sqrt{ \frac{g}{ 2 \, y_0 } }$$
$$y_0 ~=~ \frac{g}{2} \, \left( \frac{w}{v_0} \right)^2$$
$$g ~=~ 2 \, y_0 \, \left( \frac{v_0}{w} \right)^2$$
Throw distance
$$ w $$ Unit $$ \mathrm{m} $$
The throw distance (generally: flight distance) is the distance from the throw/launch point to the place where the body lands on the ground. We can also replace the root term in the formula with the flight duration \( t_{\text d} \):
\[ w ~=~ v_0 \, t_{\text d} \]
Initial speed
$$ v_0 $$ Unit $$ \frac{\mathrm m}{\mathrm s} $$
This is the speed in horizontal direction with which a body is thrown / launched.
Initial height
$$ y_0 $$ Unit $$ \mathrm{m} $$
Initial height is the distance from the throwing/launching position to the ground.
Gravitational acceleration
$$ g $$ Unit $$ \frac{\mathrm{m}}{\mathrm{s}^2} $$
Gravitational acceleration is a constant acceleration experienced by all freely falling bodies near the ground. It has the value:
$$ g ~=~ 9.8 \, \frac{\mathrm m}{\mathrm{s}^2} $$