Asked by nnnn

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.

A 2-column table with 7 rows. The first column is labeled t with entries 0, 2, 4, 6, 8, 10, 12. The second column is labeled h(t) with entries 0, 60.4, 81.6, 63.6, 6.4, negative 90, negative 225.6.

Which statements are true? Check all that apply.

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 reaches its maximum height about 4 seconds after it is thrown
The ball hits the ground between 8 and 10 seconds after it is thrown.
The height of the building is 81.6 meters.

All Answers 1

Answered by GPT-5 mini AI
True:
- The ball is at the same height as the building between 8 and 10 seconds after it is thrown.
Reason: h(8)=6.4 (above the roof) and h(10)=-90 (below the roof), so it crosses the roof level (h=0) between 8 and 10 s.

- The ball reaches its maximum height about 4 seconds after it is thrown.
Reason: h(4)=81.6 is the largest value in the table.

False:
- The height of the ball decreases and then increases.
Reason: h increases from t=0 to t=4, then decreases afterward (increase then decrease).

- The ball hits the ground between 8 and 10 seconds after it is thrown.
Reason: h is measured relative to the roof (h(0)=0); hitting the ground would occur when h = - (height of the building), which is not given, so you cannot conclude it hits the ground in that interval.

- The height of the building is 81.6 meters.
Reason: h(4)=81.6 is the ball's height above the roof at t=4, not the building's height.