Question

You shoot a water balloon out of your second story window using a water balloon launcher. The height (h) of your water balloon in feet after t seconds can be modeled by the equation: h = −16t 2 + 12t + 18. How long will it take for the water balloon to hit the ground?

Answer 1

1.5 seconds.

Explanation:

The height h of the water balloon t seconds after it is shot out of the second story building is modeled by:

`h = -16t^ 2 + 12t + 18`

The water balloon will it the ground when its height equals 0. Therefore:

`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=(6)/(4), t= -(3)/(4)\\t=1.5, t=-0.75`

Since t cannot be negative, the time it takes the balloon to hit the ground is therefore 1.5 seconds.