To find the time that it will take for an object to hit the ground, consider that the ground has a height of 0.
Since the balloon is 400 feet from the ground and the heigh of the ground is h=0, substitute s=400 and h=0 into the equation and solve for t:
[tex]\begin{gathered} h=-16t^2+s \\ \Rightarrow0=-16t^2+400 \\ \Rightarrow16t^2=400 \\ \Rightarrow t^2=\frac{400}{16} \\ \Rightarrow t^2=25 \\ \Rightarrow t=\sqrt[]{25} \\ \Rightarrow t=5 \end{gathered}[/tex]Therefore, it would take 5 seconds for the object to hit the ground.
