Question

Which equation can be used to find the time, t, it takes for the ball to reach the ground?

Answer 1

Check the picture below, well that picture is using feet, but is pretty much the same curve for meters.

notice, it hits the ground when y = 0, or h(t) = 0, thus

$\bf ~~~~~~\textit{initial velocity} \\\\ \begin{array}{llll} ~~~~~~\textit{in meters} \\\\ h(t) = -4.9t^2+v_ot+h_o \end{array} \quad \begin{cases} v_o=\stackrel{12}{\textit{initial velocity of the object}}\\\\ h_o=\stackrel{1.8}{\textit{initial height of the object}}\\\\ h=\stackrel{}{\textit{height of the object at "t" seconds}} \end{cases} \\\\\\ 0=-4.9t^2+12t+1.8\implies -4.9t^2+12t+1.8=0$