A stone is thrown horizontally with speed $v_0 = 10$ m/s from a height $h = 20$ m. Find the range of the stone (the horizontal distance from the point of release to the landing point). $g = 10$ m/s², neglect air resistance.
The flight time is determined by the height alone (vertical motion is free fall with $v_{0y} = 0$):
$$h = \frac{gt^2}{2} \Rightarrow t = \sqrt{\frac{2h}{g}} = \sqrt{\frac{2 \cdot 20}{10}} = \sqrt{4} = 2 \text{ s}$$
The horizontal motion is uniform:
$$L = v_0 t = 10 \cdot 2 = 20 \text{ m}$$
$L = 20$ m