Let's go through the statements one by one using the data provided:
1. The initial height of the ball is 96 feet.
- Referring to the table, at [tex]\( t = 0 \)[/tex], the height [tex]\( h(t) \)[/tex] is 0 feet. Therefore, this statement is false.
2. The ball will hit the ground between 2 and 3 seconds after it was thrown.
- From the table, at [tex]\( t = 5 \)[/tex], [tex]\( h(t) \)[/tex] is 0 feet, meaning the ball hits the ground at 5 seconds, not between 2 and 3 seconds. Thus, this statement is false.
3. The maximum height of the ball must be 96 feet.
- The table shows that the maximum height [tex]\( h(t) \)[/tex] of 96 feet occurs at [tex]\( t = 2 \)[/tex] and [tex]\( t = 3 \)[/tex]. Therefore, this statement is true.
4. The maximum height of the ball was reached 2.5 seconds after it was thrown.
- According to the table, the ball reaches its maximum height at [tex]\( t = 2 \)[/tex] and remains at that height until [tex]\( t = 3 \)[/tex]. There is no indication that the exact moment of maximum height occurs at [tex]\( t = 2.5 \)[/tex]. Hence, this statement is false.
Based on the analysis:
- Statement 1: False
- Statement 2: False
- Statement 3: True
- Statement 4: False
The true statement is: The maximum height of the ball must be 96 feet.
