Question 327862
{{{S(t)=-16t^2-32t+128}}}
When the wrench hits the ground, {{{S(t) = 0}}}
since the height is zero.
{{{0 =-16t^2-32t+128}}}
The minus in front of the squared term tells
me the parabola solution has a maximum peak
Divide both sides by {{{16}}}
{{{-t^2 - 2t + 8 = 0}}}
{{{t^2 + 2t - 8 = 0}}}
Complete the square
{{{t^2 + 2t + (-2/2)^2 = 8  + (-2/2)^2}}}
{{{ (t + 1)^2 = 8 + 1}}}
{{{t + 1 = 3}}}
{{{t = 2}}} sec
The wrench will hit the ground in 2 seconds