Answer:
The ball hit the ground at t=6 seconds
Step-by-step explanation:
we have
[tex]f(t)=-16t^2+96t[/tex]
where
f(t) is he height of the ball in feet
t is the time in seconds
we know that
When the ball hit the ground, the height of the ball is equal to zero
so
For f(t)=0
[tex]-16t^2+96t=0[/tex]
solve for t
Factor the leading coefficient -16t
[tex]-16t(t-6)=0[/tex]
the solutions are
t=0, t=6
Remember that
For t=0 ----> f(t)=0 is the initial height of the ball
Fort=6 sec ----> f(t)=0
therefore
The ball hit the ground at t=6 seconds
