Answer
8 seconds
Work Step by Step
We are given that the height of the football above the Colorado River at any time t can be described by the polynomial function $P(t)=-16t^{2}+10t+910$.
In order to find how long before the football lands in the river, we must find t such that $P(t)=0$.
Plug in $t=7$.
$P(7)=-16(7^{2})+10(7)+910=-16(49)+70+910=-784+70+910=196$ feet
Plug in $t=8$.
$P(8)=-16(8^{2})+10(8)+910=-16(64)+80+910=-1024+80+910=-34$ feet
Since, $P(8)$ is closer to 0, we can assume that it takes approximately 8 seconds for the ball to land in the river.
