Question

A water balloon is thrown out of a window 96 feet above the ground. The balloon is traveling downward at 16 feet per second initially. If h is the balloon’s height in feet after t seconds, then

h = -16t 2 -16t + 96,

It will take the balloon
a0 seconds to hit the ground.

Answer 1

It would take the balloon 2 seconds to hit the ground

Explanation:

They give you the actual formula of the height of the ballon as a function of time in seconds, with all the initial conditions specified in the equation, therefore all you need to do is find the time that it takes for the balloon to reach a height of zero (0) feet, making h=0 and solving for t in a quadratic equation:

`h=-16t^2-16t+96\\0=-16t^2-16t+96\\(0)/(-16) =-(16)/(-16) t^2-(16)/(-16)t+(96)/(-16)\\0=t^2+t-6\\0=(t+3)*(t-2)`

where we have factored out the trinomial as a product of two simple binomials. For such product to be zero, either t=2 seconds or t=-3 seconds. Since the time cannot be a negative number, the only viable solution we found is t=2 seconds.