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\n| t | h(t) |\n|----|----| \n| 0 | 0 |\n| 1 | 64 |\n| 2 | 96 |\n| 3 | 96 |\n| 4 | 64 |\n| 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 feet. the maximum height of the ball was reached 2.5 seconds after it was thrown.
Answer
Explanation:
Step1: Check initial height
When (t = 0), (h(0)=0), so the initial height is 0 feet, not 96 feet.
Step2: Check when ball hits ground
When (t = 5), (h(5)=0), so the ball hits the ground at (t = 5) seconds, not between 2 and 3 seconds.
Step3: Check maximum - height
The height at (t = 2) and (t = 3) is 96 feet, but we don't know if this is the maximum. Since the height is symmetric around some point (the ball goes up and then comes down), and the function is likely a quadratic (height - time relationship for a projectile under gravity), we can also note that the average of the times when the height is the same ((t = 2) and (t = 3)) gives the time of maximum height. The time of maximum height (t=\frac{2 + 3}{2}=2.5) seconds.
Answer:
The maximum height of the ball was reached 2.5 seconds after it was thrown.