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.

Question

A 2-column table with 6 rows titled Height of Ball over Time. The first column is labeled t with entries 0, 1, 2, 3, 4, 5. The second column is labeled h(t) with entries 0, 64, 96, 96, 64, 0.
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.

Answer 1

To analyze the data provided, let's look closely at the table of values:

| t (seconds) | h(t) (height in feet) | |-------------|-----------------------| | 0 | 0 | | 1 | 64 | | 2 | 96 | | 3 | 96 | | 4 | 64 | | 5 | 0 |

Now, let's evaluate each statement:

1. The initial height of the ball is 96 feet.

   • This statement is false because at \( t = 0 \), the height \( h(0) \) is 0 feet.

2. The ball will hit the ground between 2 and 3 seconds after it was thrown.

   • At \( t = 2 \) and \( t = 3 \), the height is 96 feet. At \( t = 4 \), the height is 64 feet. The ball actually hits the ground at \( t = 5 \). This statement is false.

3. The maximum height of the ball must be 96 feet.

   • The maximum height occurs at \( t = 2 \) and \( t = 3 \), and both have a height of 96 feet. Therefore, this statement is true.

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

   • The maximum height of 96 feet is reached at \( t = 2 \) and \( t = 3 \), not at 2.5 seconds. Therefore, this statement is false.

Based on this analysis, the true statement is:

The maximum height of the ball must be 96 feet.