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:$$ g ~=~ 9.8 \, \frac{\mathrm m}{\mathrm{s}^2} $$