It will reach 80 feet for the second time after 5 seconds.
We set the equation equal to 80 feet:
80= -16t² + 96t
When solving quadratics, we want it equal to 0, so we subtract 80 from both sides:
80-80= -16t² + 96t - 80
0= -16t² + 96t - 80
We use the quadratic formula to solve:
[tex]t=\frac{-96\pm \sqrt{96^2-4(-16)(-80)}}{2(-16)}
\\
\\t=\frac{-96\pm \sqrt{9216-5120}}{-32}
\\
\\t=\frac{-96\pm \sqrt{4096}}{-32}
\\
\\t=\frac{-96\pm 64}{-32}
\\
\\t=\frac{-96+64}{-32} \text{ or } 0=\frac{-96-64}{-32}
\\
\\t=1 \text{ or } t=5[/tex]
