Answer: B. 1.33 minutes
Step-by-step explanation:
We have the following equation that models the motion of the pelican:
[tex]h(t)=9t^{2}-24t+16[/tex] (1)
Where [tex]h(t)[/tex] is the height of the bird and [tex]t[/tex] is the time in minutes.
Now, if we want to know he time the pelican will land on the ground, we have to solve the equation when [tex]h(t)=0[/tex]:
[tex]0=9t^{2}-24t+16[/tex] (2)
At this point we have a quadratic equation of the form [tex]0=at^{2}+bt+c[/tex], and we have to use the quadratic formula if we want to find [tex]t[/tex]:
[tex]t=\frac{-b\pm\sqrt{b^{2}-4ac}}{2a}[/tex]
Where [tex]a=9[/tex], [tex]b=-24[/tex], [tex]c=16[/tex]
Substituting the known values:
[tex]t=\frac{-(-24)\pm\sqrt{(-24)^{2}-4(9)(16)}}{2(9)}[/tex]
Finally:
[tex]t=1.33 min[/tex] This is the time when the pelican will land on the ground
