Question
The table relates to a function h(t) that models the height of a rock t seconds after it is dropped.
A 2-column table with 5 rows. The first column is labeled t with entries 0, 0.5, 1, 1.5, 2, 2.5, 3. The second column is labeled h(t) with entries 20, 18.8, 15.1, 9, 0.4, negative 10.6, negative 24.1.
When does the rock hit the ground?
The rock hits the ground between
seconds and
seconds after it is dropped.
A 2-column table with 5 rows. The first column is labeled t with entries 0, 0.5, 1, 1.5, 2, 2.5, 3. The second column is labeled h(t) with entries 20, 18.8, 15.1, 9, 0.4, negative 10.6, negative 24.1.
When does the rock hit the ground?
The rock hits the ground between
seconds and
seconds after it is dropped.
Answers
GPT-4o mini
To determine when the rock hits the ground, we need to find when the height \( h(t) \) becomes zero. Looking at the provided values, we can analyze the height of the rock at different times.
The height \( h(t) \) is provided in the table:
- At \( t = 0 \), \( h(0) = 20 \)
- At \( t = 0.5 \), \( h(0.5) = 18.8 \)
- At \( t = 1 \), \( h(1) = 15.1 \)
- At \( t = 1.5 \), \( h(1.5) = 9 \)
- At \( t = 2 \), \( h(2) = 0.4 \)
- At \( t = 2.5 \), \( h(2.5) = -10.6 \)
- At \( t = 3 \), \( h(3) = -24.1 \)
From this data, we see:
- The rock is still above ground at \( t = 2 \) with \( h(2) = 0.4 \).
- The rock is below ground at \( t = 2.5 \) with \( h(2.5) = -10.6 \).
Since the height changes from positive to negative between \( t = 2 \) and \( t = 2.5 \), we can conclude that the rock hits the ground between these two times.
Therefore, the rock hits the ground between **2 seconds** and **2.5 seconds** after it is dropped.
The height \( h(t) \) is provided in the table:
- At \( t = 0 \), \( h(0) = 20 \)
- At \( t = 0.5 \), \( h(0.5) = 18.8 \)
- At \( t = 1 \), \( h(1) = 15.1 \)
- At \( t = 1.5 \), \( h(1.5) = 9 \)
- At \( t = 2 \), \( h(2) = 0.4 \)
- At \( t = 2.5 \), \( h(2.5) = -10.6 \)
- At \( t = 3 \), \( h(3) = -24.1 \)
From this data, we see:
- The rock is still above ground at \( t = 2 \) with \( h(2) = 0.4 \).
- The rock is below ground at \( t = 2.5 \) with \( h(2.5) = -10.6 \).
Since the height changes from positive to negative between \( t = 2 \) and \( t = 2.5 \), we can conclude that the rock hits the ground between these two times.
Therefore, the rock hits the ground between **2 seconds** and **2.5 seconds** after it is dropped.
A ball is dropped from above ground level and hits the ground sometime between 4 and 6 seconds after it is dropped. The ball's height in meters is modeled by a function h(t), where t represents time in seconds. Which table most likely relates to this function?
A 2-column table with 4 rows. The first column is labeled t with entries 0, 2, 4, 6. The second column is labeled h(t) with entries 70, 50.4, negative 8.4, negative 106.4.
A 2-column table with 4 rows. The first column is labeled t with entries 0, 2, 4, 6. The second column is labeled h(t) with entries 100, 80.4, 21.6, negative 76.4.
A 2-column table with 4 rows. The first column is labeled t with entries 0, 2, 4, 6. The second column is labeled h(t) with entries negative 150, negative 130.4, negative 71.6, 26.4.
A 2-column table with 4 rows. The first column is labeled t with entries 0, 2, 4, 6. The second column is labeled h(t) with entries 180, 160.4, 101.6, 3.6.
A 2-column table with 4 rows. The first column is labeled t with entries 0, 2, 4, 6. The second column is labeled h(t) with entries 70, 50.4, negative 8.4, negative 106.4.
A 2-column table with 4 rows. The first column is labeled t with entries 0, 2, 4, 6. The second column is labeled h(t) with entries 100, 80.4, 21.6, negative 76.4.
A 2-column table with 4 rows. The first column is labeled t with entries 0, 2, 4, 6. The second column is labeled h(t) with entries negative 150, negative 130.4, negative 71.6, 26.4.
A 2-column table with 4 rows. The first column is labeled t with entries 0, 2, 4, 6. The second column is labeled h(t) with entries 180, 160.4, 101.6, 3.6.
GPT-4o mini
To determine which table most likely relates to the function \( h(t) \) representing the height of the ball over time, we need to focus on a few key points based on the conditions provided:
1. The ball is dropped from above ground level, so the initial height \( h(0) \) should be positive (greater than zero).
2. The ball hits the ground sometime between 4 and 6 seconds, which means that \( h(4) \) should be positive and \( h(6) \) should be negative.
Let's analyze each table based on these criteria:
1. **Table 1**:
- \( h(0) = 70 \) (positive)
- \( h(4) = -8.4 \) (negative)
- \( h(6) = -106.4 \) (negative)
- **Conclusion**: This table fits the requirements. The ball is above ground initially and falls below ground level between 4 and 6 seconds.
2. **Table 2**:
- \( h(0) = 100 \) (positive)
- \( h(4) = 21.6 \) (positive)
- \( h(6) = -76.4 \) (negative)
- **Conclusion**: This table does NOT fit the requirements because the ball is still above ground at 4 seconds.
3. **Table 3**:
- \( h(0) = -150 \) (negative)
- **Conclusion**: This table does NOT fit the requirements because the starting height is below ground level.
4. **Table 4**:
- \( h(0) = 180 \) (positive)
- \( h(4) = 3.6 \) (positive)
- **Conclusion**: This table does NOT fit the requirements because the ball is still above ground at 4 seconds.
From the analysis above, only the **first table** fits all the criteria given in the problem:
- It starts at a positive height (70 meters),
- It goes below ground level between 4 and 6 seconds.
Therefore, the correct choice is **Table 1**.
1. The ball is dropped from above ground level, so the initial height \( h(0) \) should be positive (greater than zero).
2. The ball hits the ground sometime between 4 and 6 seconds, which means that \( h(4) \) should be positive and \( h(6) \) should be negative.
Let's analyze each table based on these criteria:
1. **Table 1**:
- \( h(0) = 70 \) (positive)
- \( h(4) = -8.4 \) (negative)
- \( h(6) = -106.4 \) (negative)
- **Conclusion**: This table fits the requirements. The ball is above ground initially and falls below ground level between 4 and 6 seconds.
2. **Table 2**:
- \( h(0) = 100 \) (positive)
- \( h(4) = 21.6 \) (positive)
- \( h(6) = -76.4 \) (negative)
- **Conclusion**: This table does NOT fit the requirements because the ball is still above ground at 4 seconds.
3. **Table 3**:
- \( h(0) = -150 \) (negative)
- **Conclusion**: This table does NOT fit the requirements because the starting height is below ground level.
4. **Table 4**:
- \( h(0) = 180 \) (positive)
- \( h(4) = 3.6 \) (positive)
- **Conclusion**: This table does NOT fit the requirements because the ball is still above ground at 4 seconds.
From the analysis above, only the **first table** fits all the criteria given in the problem:
- It starts at a positive height (70 meters),
- It goes below ground level between 4 and 6 seconds.
Therefore, the correct choice is **Table 1**.
nope what is the other table?? not 1
GPT-4o mini
Let's analyze the remaining tables again while keeping the criteria in mind:
1. **Table 2**:
- \( h(0) = 100 \) (positive)
- \( h(2) = 80.4 \) (positive)
- \( h(4) = 21.6 \) (positive)
- \( h(6) = -76.4 \) (negative)
- **Conclusion**: This table fits the criteria. The ball starts above ground and finally hits the ground before 6 seconds (as it is still above zero at 4 seconds but below at 6 seconds).
2. **Table 3**:
- \( h(0) = -150 \) (negative)
- **Conclusion**: This table does not fit as it starts below ground level.
3. **Table 4**:
- \( h(0) = 180 \) (positive)
- \( h(2) = 160.4 \) (positive)
- \( h(4) = 101.6 \) (positive)
- \( h(6) = 3.6 \) (positive)
- **Conclusion**: This table does not fit because it remains above ground at 4 seconds and does not hit the ground before 6 seconds.
Therefore, the second table, **Table 2**, is the only one that meets the conditions indicating that the ball is dropped from above ground level and hits the ground between 4 and 6 seconds after being dropped.
Thank you for your patience, and the correct second table related to the function is:
**Table 2**:
- \( h(0) = 100 \)
- \( h(2) = 80.4 \)
- \( h(4) = 21.6 \)
- \( h(6) = -76.4 \)
1. **Table 2**:
- \( h(0) = 100 \) (positive)
- \( h(2) = 80.4 \) (positive)
- \( h(4) = 21.6 \) (positive)
- \( h(6) = -76.4 \) (negative)
- **Conclusion**: This table fits the criteria. The ball starts above ground and finally hits the ground before 6 seconds (as it is still above zero at 4 seconds but below at 6 seconds).
2. **Table 3**:
- \( h(0) = -150 \) (negative)
- **Conclusion**: This table does not fit as it starts below ground level.
3. **Table 4**:
- \( h(0) = 180 \) (positive)
- \( h(2) = 160.4 \) (positive)
- \( h(4) = 101.6 \) (positive)
- \( h(6) = 3.6 \) (positive)
- **Conclusion**: This table does not fit because it remains above ground at 4 seconds and does not hit the ground before 6 seconds.
Therefore, the second table, **Table 2**, is the only one that meets the conditions indicating that the ball is dropped from above ground level and hits the ground between 4 and 6 seconds after being dropped.
Thank you for your patience, and the correct second table related to the function is:
**Table 2**:
- \( h(0) = 100 \)
- \( h(2) = 80.4 \)
- \( h(4) = 21.6 \)
- \( h(6) = -76.4 \)
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.
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.
GPT-4o mini
Let's analyze the height data provided in the table of the ball's height \( h(t) \) over time \( t \).
Given data:
- At \( t = 0 \), \( h(0) = 0 \)
- At \( t = 2 \), \( h(2) = 60.4 \)
- At \( t = 4 \), \( h(4) = 81.6 \)
- At \( t = 6 \), \( h(6) = 63.6 \)
- At \( t = 8 \), \( h(8) = 6.4 \)
- At \( t = 10 \), \( h(10) = -90 \)
- At \( t = 12 \), \( h(12) = -225.6 \)
Now, let’s evaluate each statement:
1. **The ball is at the same height as the building between 8 and 10 seconds after it is thrown.**
- At \( t = 8 \), \( h(8) = 6.4 \) (above ground)
- At \( t = 10 \), \( h(10) = -90 \) (below ground)
- The ball does not return to the height of the building during this interval, so this statement **is false**.
2. **The height of the ball decreases and then increases.**
- From \( t = 0 \) to \( t = 4 \), the height increases from \( 0 \) to \( 81.6 \).
- From \( t = 4 \) to \( t = 6\), the height decreases from \( 81.6 \) to \( 63.6 \).
- From \( t = 6 \) to \( t = 8\), the height decreases from \( 63.6 \) to \( 6.4 \).
- Therefore, the height decreases until \( t = 8 \). So, the overall trend is not "decreases and then increases." Thus, this statement **is false**.
3. **The ball reaches its maximum height about 4 seconds after it is thrown.**
- The maximum height occurs at \( t = 4\) where \( h(4) = 81.6 \). This statement **is true**.
4. **The ball hits the ground between 8 and 10 seconds after it is thrown.**
- The ball is above ground at \( t = 8 \) with \( h(8) = 6.4 \) and falls below ground at \( t = 10 \) with \( h(10) = -90 \). Since the height changes from positive to negative, it indeed hits the ground between these times. This statement **is true**.
5. **The height of the building is 81.6 meters.**
- The height \( h(0) = 0 \) represents the starting point of the ball when thrown from the roof. Since the maximum height achieved by the ball (81.6 meters) is an indication of the height reached above the initial height of the building and not the actual height of the building. Therefore, this statement **is false**.
### Summary of True Statements:
- The ball reaches its maximum height about 4 seconds after it is thrown. **(True)**
- The ball hits the ground between 8 and 10 seconds after it is thrown. **(True)**
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.
Given data:
- At \( t = 0 \), \( h(0) = 0 \)
- At \( t = 2 \), \( h(2) = 60.4 \)
- At \( t = 4 \), \( h(4) = 81.6 \)
- At \( t = 6 \), \( h(6) = 63.6 \)
- At \( t = 8 \), \( h(8) = 6.4 \)
- At \( t = 10 \), \( h(10) = -90 \)
- At \( t = 12 \), \( h(12) = -225.6 \)
Now, let’s evaluate each statement:
1. **The ball is at the same height as the building between 8 and 10 seconds after it is thrown.**
- At \( t = 8 \), \( h(8) = 6.4 \) (above ground)
- At \( t = 10 \), \( h(10) = -90 \) (below ground)
- The ball does not return to the height of the building during this interval, so this statement **is false**.
2. **The height of the ball decreases and then increases.**
- From \( t = 0 \) to \( t = 4 \), the height increases from \( 0 \) to \( 81.6 \).
- From \( t = 4 \) to \( t = 6\), the height decreases from \( 81.6 \) to \( 63.6 \).
- From \( t = 6 \) to \( t = 8\), the height decreases from \( 63.6 \) to \( 6.4 \).
- Therefore, the height decreases until \( t = 8 \). So, the overall trend is not "decreases and then increases." Thus, this statement **is false**.
3. **The ball reaches its maximum height about 4 seconds after it is thrown.**
- The maximum height occurs at \( t = 4\) where \( h(4) = 81.6 \). This statement **is true**.
4. **The ball hits the ground between 8 and 10 seconds after it is thrown.**
- The ball is above ground at \( t = 8 \) with \( h(8) = 6.4 \) and falls below ground at \( t = 10 \) with \( h(10) = -90 \). Since the height changes from positive to negative, it indeed hits the ground between these times. This statement **is true**.
5. **The height of the building is 81.6 meters.**
- The height \( h(0) = 0 \) represents the starting point of the ball when thrown from the roof. Since the maximum height achieved by the ball (81.6 meters) is an indication of the height reached above the initial height of the building and not the actual height of the building. Therefore, this statement **is false**.
### Summary of True Statements:
- The ball reaches its maximum height about 4 seconds after it is thrown. **(True)**
- The ball hits the ground between 8 and 10 seconds after it is thrown. **(True)**
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.
one more answer? or one of the two statements are WRONG
GPT-4o mini
Let’s take another close look at the statements and the corresponding data, to ensure accuracy. Here’s the data again for reference:
- At \( t = 0 \), \( h(0) = 0 \)
- At \( t = 2 \), \( h(2) = 60.4 \)
- At \( t = 4 \), \( h(4) = 81.6 \)
- At \( t = 6 \), \( h(6) = 63.6 \)
- At \( t = 8 \), \( h(8) = 6.4 \)
- At \( t = 10 \), \( h(10) = -90 \)
- At \( t = 12 \), \( h(12) = -225.6 \)
Now, let's re-evaluate each statement carefully:
1. **The ball is at the same height as the building between 8 and 10 seconds after it is thrown.**
- **False**: At \( t = 8 \), the height is \( 6.4 \) meters (above ground), and at \( t = 10\), the height is \(-90\) meters (below ground). Thus, it does not reach the height of the building (which would be at \( h(0) = 0\)) during that time.
2. **The height of the ball decreases and then increases.**
- **True**: The ball's height rises from \( 0\) to \( 81.6\) meters at \( t = 4 \) (increasing). It then decreases to \( 63.6 \) at \( t = 6\), and further down to \( 6.4\) at \( t = 8\). So, the ball indeed has a decreasing phase (from \( t = 4\) to \( t = 8 \)), and it does not rise again until hitting the ground, and thus remains a low height from then onwards. **(However, in the context of overall motion before hitting the ground, this statement can be considered false because it does not technically increase after it decreases)**.
3. **The ball reaches its maximum height about 4 seconds after it is thrown.**
- **True**: The maximum height of \( 81.6\) is indeed achieved at \( t = 4\).
4. **The ball hits the ground between 8 and 10 seconds after it is thrown.**
- **True**: The height is positive at \( t = 8\) and negative at \( t = 10\), indicating that the ball must have hit the ground between these times.
5. **The height of the building is 81.6 meters.**
- **False**: The ball starts at \( h(0) = 0\) meters, which indicates that the height above ground where the ball was thrown is at roof height at that moment. The height of the ball's peak does not correspond to the actual height of the building.
### Summary:
1. **False**
2. **False (on closer re-evaluation)**
3. **True**
4. **True**
5. **False**
The correct 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."
So it appears **statement 2** should be corrected to **false**, as the ball never increases from after reaching its peak. Thank you for your patience!
- At \( t = 0 \), \( h(0) = 0 \)
- At \( t = 2 \), \( h(2) = 60.4 \)
- At \( t = 4 \), \( h(4) = 81.6 \)
- At \( t = 6 \), \( h(6) = 63.6 \)
- At \( t = 8 \), \( h(8) = 6.4 \)
- At \( t = 10 \), \( h(10) = -90 \)
- At \( t = 12 \), \( h(12) = -225.6 \)
Now, let's re-evaluate each statement carefully:
1. **The ball is at the same height as the building between 8 and 10 seconds after it is thrown.**
- **False**: At \( t = 8 \), the height is \( 6.4 \) meters (above ground), and at \( t = 10\), the height is \(-90\) meters (below ground). Thus, it does not reach the height of the building (which would be at \( h(0) = 0\)) during that time.
2. **The height of the ball decreases and then increases.**
- **True**: The ball's height rises from \( 0\) to \( 81.6\) meters at \( t = 4 \) (increasing). It then decreases to \( 63.6 \) at \( t = 6\), and further down to \( 6.4\) at \( t = 8\). So, the ball indeed has a decreasing phase (from \( t = 4\) to \( t = 8 \)), and it does not rise again until hitting the ground, and thus remains a low height from then onwards. **(However, in the context of overall motion before hitting the ground, this statement can be considered false because it does not technically increase after it decreases)**.
3. **The ball reaches its maximum height about 4 seconds after it is thrown.**
- **True**: The maximum height of \( 81.6\) is indeed achieved at \( t = 4\).
4. **The ball hits the ground between 8 and 10 seconds after it is thrown.**
- **True**: The height is positive at \( t = 8\) and negative at \( t = 10\), indicating that the ball must have hit the ground between these times.
5. **The height of the building is 81.6 meters.**
- **False**: The ball starts at \( h(0) = 0\) meters, which indicates that the height above ground where the ball was thrown is at roof height at that moment. The height of the ball's peak does not correspond to the actual height of the building.
### Summary:
1. **False**
2. **False (on closer re-evaluation)**
3. **True**
4. **True**
5. **False**
The correct 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."
So it appears **statement 2** should be corrected to **false**, as the ball never increases from after reaching its peak. Thank you for your patience!
but its wrong there must be one more or one of the 2 statements are WRONG if they are certainly right then get one more answer
GPT-4o mini
Let's reevaluate the statements and the data in detail to clarify everything.
### Given Data:
- \( t = 0 \): \( h(0) = 0 \)
- \( t = 2 \): \( h(2) = 60.4 \)
- \( t = 4 \): \( h(4) = 81.6 \)
- \( t = 6 \): \( h(6) = 63.6 \)
- \( t = 8 \): \( h(8) = 6.4 \)
- \( t = 10 \): \( h(10) = -90 \)
- \( t = 12 \): \( h(12) = -225.6 \)
### Evaluating Each Statement Again:
1. **The ball is at the same height as the building between 8 and 10 seconds after it is thrown.**
- **True or False?** The building is at \( h(0) = 0 \). At \( t = 8 \), \( h(8) = 6.4\) (which is above ground) and \( h(10) = -90\) (which is below ground). Thus, the ball is not at the same height as the building at this time, so this statement is **False**.
2. **The height of the ball decreases and then increases.**
- **True or False?** The ball's height increases from \( 0 \) at \( t = 0 \) to \( 81.6 \) at \( t = 4 \) and then decreases to \( 63.6 \) at \( t = 6 \), and then further decreases to \( 6.4 \) at \( t = 8 \). There is no increase after that – it does not rise again before hitting the ground. So, this statement is **False**.
3. **The ball reaches its maximum height about 4 seconds after it is thrown.**
- **True or False?** The maximum height of the ball is indeed \( 81.6 \) at \( t = 4 \). This statement is **True**.
4. **The ball hits the ground between 8 and 10 seconds after it is thrown.**
- **True or False?** The ball’s height is above ground at \( t = 8 \) and is below ground (negative) at \( t = 10 \), indicating that the ball did hit the ground between these two times. This statement is **True**.
5. **The height of the building is 81.6 meters.**
- **True or False?** The building's height cannot be inferred from the maximum height of the ball. The ball starts from \( 0 \) meters at \( t = 0 \) (roof level or ground level). Thus, this statement is **False**.
### Summary of Statements:
- **1**: False
- **2**: False
- **3**: True
- **4**: True
- **5**: False
### Which Statements are True?
Only statements **3** and **4** are true. All other statements are false.
To clarify:
- **The ball is at the same height as the building between 8 and 10 seconds after it is thrown** - **False**
- **The height of the ball decreases and then increases** - **False**
- **The ball reaches its maximum height about 4 seconds after it is thrown** - **True**
- **The ball hits the ground between 8 and 10 seconds after it is thrown** - **True**
- **The height of the building is 81.6 meters** - **False**
Thank you for your patience! The correct true statements are **3** and **4**.
### Given Data:
- \( t = 0 \): \( h(0) = 0 \)
- \( t = 2 \): \( h(2) = 60.4 \)
- \( t = 4 \): \( h(4) = 81.6 \)
- \( t = 6 \): \( h(6) = 63.6 \)
- \( t = 8 \): \( h(8) = 6.4 \)
- \( t = 10 \): \( h(10) = -90 \)
- \( t = 12 \): \( h(12) = -225.6 \)
### Evaluating Each Statement Again:
1. **The ball is at the same height as the building between 8 and 10 seconds after it is thrown.**
- **True or False?** The building is at \( h(0) = 0 \). At \( t = 8 \), \( h(8) = 6.4\) (which is above ground) and \( h(10) = -90\) (which is below ground). Thus, the ball is not at the same height as the building at this time, so this statement is **False**.
2. **The height of the ball decreases and then increases.**
- **True or False?** The ball's height increases from \( 0 \) at \( t = 0 \) to \( 81.6 \) at \( t = 4 \) and then decreases to \( 63.6 \) at \( t = 6 \), and then further decreases to \( 6.4 \) at \( t = 8 \). There is no increase after that – it does not rise again before hitting the ground. So, this statement is **False**.
3. **The ball reaches its maximum height about 4 seconds after it is thrown.**
- **True or False?** The maximum height of the ball is indeed \( 81.6 \) at \( t = 4 \). This statement is **True**.
4. **The ball hits the ground between 8 and 10 seconds after it is thrown.**
- **True or False?** The ball’s height is above ground at \( t = 8 \) and is below ground (negative) at \( t = 10 \), indicating that the ball did hit the ground between these two times. This statement is **True**.
5. **The height of the building is 81.6 meters.**
- **True or False?** The building's height cannot be inferred from the maximum height of the ball. The ball starts from \( 0 \) meters at \( t = 0 \) (roof level or ground level). Thus, this statement is **False**.
### Summary of Statements:
- **1**: False
- **2**: False
- **3**: True
- **4**: True
- **5**: False
### Which Statements are True?
Only statements **3** and **4** are true. All other statements are false.
To clarify:
- **The ball is at the same height as the building between 8 and 10 seconds after it is thrown** - **False**
- **The height of the ball decreases and then increases** - **False**
- **The ball reaches its maximum height about 4 seconds after it is thrown** - **True**
- **The ball hits the ground between 8 and 10 seconds after it is thrown** - **True**
- **The height of the building is 81.6 meters** - **False**
Thank you for your patience! The correct true statements are **3** and **4**.