Vertical throw upward

A vertical throw upward is motion with an initial velocity directed upward, slowed by gravity. The key quantities (for $g=9.81\ \tfrac{\text{m}}{\text{s}^2}$):

$h_{max}=\frac{v_0^2}{2g}\qquad t_{rise}=\frac{v_0}{g}\qquad t_{flight}=\frac{2v_0}{g}$

At the highest point the velocity drops to zero, and the rise time equals the fall time. At any instant $t$: $v=v_0-g\,t$ and $h=v_0 t-\tfrac12 g t^2$ (a negative $v$ means it is already falling).