a ball is thrown straight up into the air. the table shows the data collected over t seconds, where h(t) is…

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 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 feet. the maximum height of the ball was reached 2.5 seconds after it was thrown.\n| t | h(t) |\n|----|----|\n| 0 | 0 |\n| 1 | 64 |\n| 2 | 96 |\n| 3 | 96 |\n| 4 | 64 |\n| 5 | 0 |
Answer
Answer:
The ball will hit the ground between 2 and 3 seconds after it was thrown.
Explanation:
Step1: Analyze initial height
When (t = 0), (h(0)=0), so initial height is 0 feet, not 96 feet.
Step2: Check maximum - height
The height at (t = 2) and (t = 3) is 96 feet, but we can't be sure it's the maximum without more data. Also, we don't know if the maximum was reached at (t = 2.5) seconds.
Step3: Analyze when it hits the ground
The ball's height (h(t)) is 0 at (t = 0) (start) and (t = 5). Since the height is positive at (t = 2) ((h(2)=96)) and (t = 3) ((h(3)=96)), and then becomes 0 at (t = 5), it must hit the ground between 2 and 3 seconds after it was thrown.