Question

a ball is thrown straight up into the air. the table shows the data collected over t seconds, where h(t) is the height of the ball, in feet. height of ball over time

t	h(t)
0	0
1	64
2	96
3	96
4	64
5	0

which statement is true? the initial height of the ball is 96 feet. the ball will hit the ground between 2 and 3 seconds after it was thrown. the maximum height of the ball must be 96. the maximum height of the ball was reache seconds after it was thrown.

Explanation:

Step1: Analyze initial height

When $t = 0$, $h(0)=0$. So the initial height is 0 feet, not 96 feet.

Step2: Check when ball hits ground

The ball hits the ground when $h(t)=0$. We see $h(0) = 0$ (initial throw) and $h(5)=0$. So it hits the ground at $t = 5$ seconds, not between 2 and 3 seconds.

Step3: Analyze maximum height

The height values are $h(1)=64$, $h(2)=96$, $h(3)=96$, $h(4)=64$. The maximum height is 96 feet which occurs at $t = 2$ and $t = 3$ seconds.

Answer:

The maximum height of the ball must be 96 feet.