Answer
a) The height of the ball is 48 feet after 1 second and after 3 seconds.
b) The ball hits the ground after $4$ seconds.
Maximum height: $64$ feet
Work Step by Step
a) Given that $h(t)=-16 t^2+64 t$, we have
$$
\begin{aligned}
& h(1)=-16(1)^2+64(1)=48 \\
& h(3)=-16(3)^2+64(3)=48
\end{aligned}
$$
The height of the ball is 48 feet after 1 second and after 3 seconds.
b) We sketch the graph of the function.
From the graph we notice that the ball hits the ground after $4$ seconds and that its maximum height is $64$ feet.
