Answer:
[tex]t= 6\ s[/tex]
Step-by-step explanation:
We know that the equation that models the height of the ball as a function of time is [tex]h(t) = -16t ^ 2 + 80t + 96[/tex].
Where the initial speed is 80 feet.
When the ball lands on the ground, its height will be [tex]h(t) = 0[/tex].
So to know how long it will take the ball to reach the ground, equal h (t) to zero and solve for t.
[tex]-16t ^ 2 + 80t + 96 = 0[/tex]
To solve this quadratic equation we use the quadratic formula.
For an equation of the form:
[tex]at^2 +bt +c[/tex]
The quadratic formula is:
[tex]t=\frac{-b\±\sqrt{b^2 -4ac}}{2a}[/tex]
In this case
[tex]a =-16\\b = 80\\c =96[/tex]
Then
[tex]t=\frac{-80\±\sqrt{80^2 -4(-16)(96)}}{2(-16)}[/tex]
[tex]t_1=-1\\\\t_2=6[/tex]
We take the positive solution
[tex]t= 6\ s[/tex]
