Answer:
1.5 seconds.
Step-by-step explanation:
The height h of the water balloon t seconds after it is shot out of the second story building is modeled by:
[tex]h = -16t^ 2 + 12t + 18[/tex]
The water balloon will it the ground when its height equals 0. Therefore:
[tex]h = -16t^ 2 + 12t + 18=0\\ -16t^ 2 + 12t + 18=0\\$We solve for t\\-16t^ 2 + 24t-12t + 18=0\\-4t(4t-6)-3(4t-6)=0\\(4t-6)(-4t-3)=0\\4t-6=0, -4t-3=0\\t=\frac{6}{4}, t= -\frac{3}{4}\\t=1.5, t=-0.75[/tex]
Since t cannot be negative, the time it takes the balloon to hit the ground is therefore 1.5 seconds.
