Question

a ball rolls off a 2 meter counter at .5m/s how far from the counter does the ball land

Answer 1

Let's first find the time that the ball takes to reach the ground:

$$y=\dfrac{1}{2}gt^2,$$ $$t=\sqrt{\dfrac{2y}{g}}=\sqrt{\dfrac{2\cdot2\ m}{9.8\ \dfrac{m}{s^2}}}=0.64\ s.$$

Finally, we can find the distance from the counter to the place where the ball lands:

$$x=v_{0x}t=0.5\ \dfrac{m}{s}\cdot0.64\ s=0.32\ m.$$