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 hits the ground at h=0

0=-16t^2-16t+96
undistribute -16
0=-16(t^2+t-6)
factor
0=-16(t-2)(t+3)
set to zero
0=t-2
2=t

t+3=0
t=-3, nope, we can't have negative time

at t=2, or 2 seconds

Answer 2

2 seconds

Explanation:

Given :
`h = -16t^2 -16t + 96`

To Find: after how many seconds it will hit the ground?

Solution:

The height of the balloon is given at time t :
`h = -16t^2 -16t + 96`

Now we re supposed to find after how many seconds it will hit the ground i.e. height will be 0 , h=0

Substitute h = 0 in the equation

`0 = -16t^2 -16t + 96`

`0 = -16(t-2)(t+3)`

`t=2,-3`

Since the time cannot be negative

So, it will hit the ground after 2 seconds .