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|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|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

When (t = 5), (h(5)=0), so the ball hits the ground at (t = 5) seconds, not between 2 and 3 seconds.

Step3: Analyze maximum - height time

The height is 96 feet at (t = 2) and (t = 3). Since the function of the height of a projectile is a parabola (symmetric), the maximum occurs at (t=\frac{2 + 3}{2}=2.5) seconds. Also, we can observe the symmetry of the data values. The height values increase from (t = 0) to some point and then decrease symmetrically.

Answer:

The maximum height of the ball was reached 2.5 seconds after it was thrown.