Question

If an object is dropped from a height of 85 feet, the function h(t)=-16t^2+85, gives the height of the object after t seconds approximately when will the object hit the ground

Answer 1

The object will hit the ground once the height equals to zero.

$h(t)=-16t^2+85 \\0=-16t^2+85 \\16t^2=85 \\t^2=\frac{85}{16} \\t=\sqrt{\frac{85}{16}}=\pm\frac{\sqrt{85}}{4}$

The negative answer does not fit the condition of the problem $\Rightarrow$ the answer is $\frac{\sqrt{85}}{4}\approx2.31 \ seconds$.