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. 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. 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 |
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
The ball hits the ground when (h(t)=0). We see (h(0) = 0) (initial - start) and (h(5)=0), so it hits the ground at (t = 5) seconds, not between 2 and 3 seconds.
Step3: Check maximum height
The height values are (h(0)=0), (h(1) = 64), (h(2)=96), (h(3)=96), (h(4)=64), (h(5)=0). The maximum height is 96 feet.
Step4: Check time of maximum - height
The height is 96 feet at (t = 2) and (t = 3) seconds, not at (t=2.5) seconds.
Answer:
The maximum height of the ball must be 96 feet.