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.\nheight 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 |\nwhich statement is true?\nthe initial height of the ball is 96 feet.\nthe ball will hit the ground between 2 and 3 seconds after it was thrown.\nthe maximum height of the ball must be 96 feet.\nthe maximum height of the ball was reached 2.5 seconds after it was thrown.

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.\nheight 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 |\nwhich statement is true?\nthe initial height of the ball is 96 feet.\nthe ball will hit the ground between 2 and 3 seconds after it was thrown.\nthe maximum height of the ball must be 96 feet.\nthe 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

The ball hits the ground when (h(t)=0). We see (h(0) = 0) (start - not hitting ground after being thrown) 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 ball reaches 96 feet at (t = 2) seconds and (t = 3) seconds, not at (t=2.5) seconds.

Answer:

The maximum height of the ball must be 96 feet.