To determine the most likely table that models the function \( h(t) \), representing the height of the ball as it falls, we need to consider that the ball is dropped from above ground level and hits the ground sometime between 4 and 6 seconds. Therefore, at \( t = 4 \) to \( t = 6 \), the height \( h(t) \) should be at or below 0 (the ground level).
Let's analyze the given tables:
1. **First table:**
```
t | h(t)
0 | 70
2 | 50.4
4 | -8.4
6 | -106.4
```
- \( h(4) = -8.4 \)
- \( h(6) = -106.4 \)
- The ball hits the ground between 4 and 6 seconds because \( h(4) \) is slightly below 0.
2. **Second table:**
```
t | h(t)
0 | 100
2 | 80.4
4 | 21.6
6 | -76.4
```
- \( h(4) = 21.6 \)
- \( h(6) = -76.4 \)
- The ball is still above the ground at \( t = 4 \), which doesn’t fit the description that it hits the ground between 4 and 6 seconds.
3. **Third table:**
```
t | h(t)
0 | -150
2 | -130.4
4 | -71.6
6 | -26.4
```
- \( h(t) \) starts below 0, which does not make sense as the ball starts above ground level.
4. **Fourth table:**
```
t | h(t)
0 | 180
2 | 160.4
4 | 101.6
6 | 3.6
```
- \( h(4) = 101.6 \)
- \( h(6) = 3.6 \)
- The ball is still above the ground at both \( t = 4 \) and \( t = 6 \), which doesn’t fit hitting the ground between 4 and 6 seconds.
**Conclusion:** The first table most likely relates to the function \( h(t) \), given the ball hits the ground sometime between 4 and 6 seconds after it is dropped, as this table shows the height at −8.4 meters at \( t = 4 \) and −106.4 meters at \( t = 6 \). The other tables either do not hit the ground in the specified time or start below ground level.
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.
1 answer