Answer:
The ball will hit the ground after 6 seconds
Step-by-step explanation:
Function Modeling
The following function models the heigh of the ball in feet kicked by Tanya after t seconds:
[tex]h(t)=-16t^2+96t[/tex]
Note that if t=0, the ball has a height of h=0, which means it's kicked from the ground level.
We must find another value for t when the ball hits the ground. That will be done by equating the quadratic function to 0 and find the values of t
[tex]-16t^2+96t=0[/tex]
Factoring
[tex]t(-16t+96)=0[/tex]
This leads to two answers, the first one is:
[tex]t=0[/tex]
which we had already talked before, and the other comes from
[tex]-16t+96=0[/tex]
Solving for t
[tex]-16t=-96[/tex]
[tex]t=-96/(-16)=6 \ s[/tex]
The ball will hit the ground after 6 seconds
