Question

the table represents the height of a ball thrown up from the roof of a building, h(t), in meters, t seconds after it is thrown upward. analyzing a table and interpreting in context. the ball is at the same height as the building between 8 and 10 seconds after it is thrown. the height of the ball decreases and then increases. the ball hits the ground between 8 and 10 seconds after it is thrown. the height of the building is 81.6 meters. the ball reaches its maximum height about 4 seconds after it is thrown.

Explanation:

We analyze the table of the ball's height \(h(t)\) over time \(t\). At \(t = 0\), the ball is at the roof height. As \(t\) increases, the height first increases (going up) and then decreases (coming down). When \(t = 4\), the height \(h(4)=81.6\) which seems to be the maximum height. At \(t = 8\), \(h(8) = 6.4\) and at \(t = 10\), \(h(10)= - 90\) (negative means below the starting - point, likely hitting the ground). The height of the building is \(h(0)=0\) (the starting - point for the ball's motion from the roof).

Answer:

1. The ball reaches its maximum height about 4 seconds after it is thrown.
2. The ball hits the ground between 8 and 10 seconds after it is thrown.
3. The height of the ball decreases and then increases is incorrect. It increases first and then decreases.
4. The height of the building is not 81.6 meters. The height of the building is the initial height \(h(0) = 0\) (measured from the roof where the ball is thrown).
5. The ball is not at the same height as the building between 8 and 10 seconds. At \(t = 8\) and \(t = 10\), the ball is either above or below the building level (starting - point). So the correct statements are: "The ball reaches its maximum height about 4 seconds after it is thrown" and "The ball hits the ground between 8 and 10 seconds after it is thrown".