thanks
a) the ball hits the ground when:Originally Posted by JohnSena
$\displaystyle
f(t)=-16t^2+96t+6=0
$
This will have two roots, one positive and the other negative, the
negative root is unphysical but the positive one is what you want.
The roots are:
$\displaystyle
-0.06186, 6.06186
$
So the ball is in the air $\displaystyle \approx 6.06$seconds.
b) The maximum height is achieved when $\displaystyle f(x)$ is
a maximum. As this is a quadratic we know this occurs midway
between the roots, so it occurs at $\displaystyle (-0.06186+6.06186)/2=3$,
so the maximum height is:
$\displaystyle
f(3)=16\ 3^2+96\ 3+6=438$ feet.
c) Already answered at $\displaystyle t=3$seconds.
RonL