To determine which statements are true, let's analyze the given data in the table:
\[
\begin{array}{|c|c|}
\hline
t (\text{seconds}) & h(t) (\text{meters}) \\
\hline
0 & 0 \\
2 & 60.4 \\
4 & 81.6 \\
6 & 63.6 \\
8 & 6.4 \\
10 & -90 \\
12 & -225.6 \\
\hline
\end{array}
\]
Using this data, let's evaluate each of the given statements:
1. **The ball is at the same height as the building between 8 and 10 seconds after it is thrown.**
- At \( t = 8 \) seconds, \( h(t) = 6.4 \) meters.
- At \( t = 10 \) seconds, \( h(t) = -90 \) meters.
- Given that heights are listed, the ball has already started going below the original height at these times. Hence, it seems the ball was at the same height as the building much earlier.
- **False.**
2. **The height of the ball decreases and then increases.**
- From \( t = 0 \) to \( t = 4 \) seconds, the height increases: \( 0 \rightarrow 60.4 \rightarrow 81.6 \).
- From \( t = 4 \) to \( t = 12 \) seconds, the height decreases: \( 81.6 \rightarrow 63.6 \rightarrow 6.4 \rightarrow -90 \rightarrow -225.6 \).
- The height only increases initially till \( t \) = 4 seconds and continues decreasing afterward. There is no increase after the initial rise.
- **False.**
3. **The ball reaches its maximum height about 4 seconds after it is thrown.**
- The maximum height listed in the table is indeed at \( t = 4 \) seconds, where \( h(t) = 81.6 \) meters.
- **True.**
4. **The ball hits the ground between 8 and 10 seconds after it is thrown.**
- The ground level corresponds to \( h(t) = 0 \) meters.
- At \( t = 8 \) seconds, \( h(t) = 6.4 \) meters.
- At \( t = 10 \) seconds, \( h(t) = -90 \) meters.
- The ball must have passed through the ground level between \( t = 8 \) and \( t = 10 \) seconds.
- **True.**
5. **The height of the building is 81.6 meters.**
- From the table, \( h(t) \) at \( t = 0 \) seconds is 0 meters, suggesting this is the initial point or roof of the building.
- Given that the ball reaches 81.6 meters above the roof cannot be the height of the building but rather the maximum height reached by the ball above the starting point.
- **False.**
Based on the analyzed data, the true statements are:
- 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 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.
1 answer