Based on the provided table and data:
[tex]\[
\begin{array}{|c|c|c|c|c|c|}
\hline
\text{Time (sec)} & 0 & 1 & 2 & 3 & 4 \\
\hline
\text{Height (ft)} & 11 & 59 & 75 & 59 & 11 \\
\hline
\end{array}
\][/tex]
Let's analyze the information step-by-step:
1. Identify the recorded times and their corresponding heights:
- At [tex]\( t = 0 \)[/tex] seconds, the height is [tex]\( 11 \)[/tex] feet.
- At [tex]\( t = 1 \)[/tex] second, the height is [tex]\( 59 \)[/tex] feet.
- At [tex]\( t = 2 \)[/tex] seconds, the height is [tex]\( 75 \)[/tex] feet.
- At [tex]\( t = 3 \)[/tex] seconds, the height is [tex]\( 59 \)[/tex] feet.
- At [tex]\( t = 4 \)[/tex] seconds, the height is [tex]\( 11 \)[/tex] feet.
2. Determine the maximum height:
- From the recorded heights [tex]\( 11, 59, 75, 59, 11 \)[/tex] feet, it is clear that the maximum height is [tex]\( 75 \)[/tex] feet.
3. Find the time at which the maximum height was reached:
- The maximum height of [tex]\( 75 \)[/tex] feet occurs at [tex]\( t = 2 \)[/tex] seconds.
Now, let's evaluate each of the provided statements:
1. The ball lands on the ground at 4 seconds.
- This statement is incorrect because the table shows the ball's height is [tex]\( 11 \)[/tex] feet at [tex]\( 4 \)[/tex] seconds, not on the ground.
2. The ball reaches a maximum height of 11 feet.
- This statement is incorrect because the maximum height reached is [tex]\( 75 \)[/tex] feet, not [tex]\( 11 \)[/tex] feet.
3. The ball was launched from a height of 0 feet.
- This statement is incorrect because the initial height at [tex]\( 0 \)[/tex] seconds is [tex]\( 11 \)[/tex] feet.
4. The ball reaches its maximum height at 2 seconds.
- This statement is correct because the maximum height of [tex]\( 75 \)[/tex] feet was reached at [tex]\( 2 \)[/tex] seconds.
Therefore, the valid conclusion based on the data provided is:
4. The ball reaches its maximum height at 2 seconds.
