Answer:
9 feet
Step-by-step explanation:
To determine Adam's height above the water when he catches the frisbee, we can set the two functions equal to each other, solve for t, and then substitute the found value of t into function h(t).
Set h(t) and f(t) equal to each other:
[tex]-t^2 + 2t + 12 = 2t + 3[/tex]
Solve for t:
[tex]-t^2 + 2t + 12 -2t-12= 2t + 3-2t-12[/tex]
[tex]-t^2 = -9[/tex]
[tex]t^2=9[/tex]
[tex]\sqrt{t^2}=\sqrt{9}[/tex]
[tex]t=\pm 3[/tex]
As time is positive only, the time at which Adam catches the frisbee is 3 seconds.
To find the height, substitute t = 3 into function h(t):
[tex]h(3)=-(3)^2+2(3)+12[/tex]
[tex]h(3)=-9+6+12[/tex]
[tex]h(3)=9[/tex]
Therefore, Adam is 9 feet above the water when he catches the frisbee.
