Question
A ball is thrown into the air from the edge of a 48-foot-high cliff so that it eventually lands on the ground. The graph below shows the height, y
, of the ball from he ground after x
seconds.
(1 point)
Responses
0<x<5.5
0<x<5.5
0≤x≤2.5
0≤x≤2.5
x≥2
x is greater than or equal to 2
2.5<x<5.5
, of the ball from he ground after x
seconds.
(1 point)
Responses
0<x<5.5
0<x<5.5
0≤x≤2.5
0≤x≤2.5
x≥2
x is greater than or equal to 2
2.5<x<5.5
Answers
GPT-4o mini
To determine the correct response for the provided options regarding the height of the ball thrown from a 48-foot-high cliff, we need to analyze the behavior of the height function \( y \) over time \( x \).
1. **0 < x < 5.5**: This suggests that the ball is at a height above ground for the entirety of this interval. This may be true but doesn’t specify the behavior near the endpoints, particularly when it lands.
2. **0 ≤ x ≤ 2.5**: This option implies that the ball is within the given height range during this time, but it doesn't account for when the ball likely reaches its peak and then starts descending.
3. **x ≥ 2**: This indicates that after 2 seconds, the ball is still above ground, but it does not specify when it reaches ground height.
4. **2.5 < x < 5.5**: This suggests that after 2.5 seconds, the ball is still in the air (height above zero) until around 5.5 seconds.
Based on common projectile motion behavior, the ball will reach a maximum height shortly before it starts to descend and touchdown. If the ball is thrown from 48 feet, it might take it around 2.5 seconds to hit the peak and then descend.
Considering all options:
- **0 < x < 5.5** may be too broad.
- **0 ≤ x ≤ 2.5** likely covers the ascent phase only.
- **x ≥ 2** captures some of the descent phase.
- **2.5 < x < 5.5** is reasonable as it likely refers to the time the ball continues to descend after peak height(around 2.5) to landing.
Without a specific graph to analyze further, I recommend choosing **2.5 < x < 5.5** as this range likely corresponds to when the ball is falling after reaching its peak height, assuming it lands on the ground after 5.5 seconds.
1. **0 < x < 5.5**: This suggests that the ball is at a height above ground for the entirety of this interval. This may be true but doesn’t specify the behavior near the endpoints, particularly when it lands.
2. **0 ≤ x ≤ 2.5**: This option implies that the ball is within the given height range during this time, but it doesn't account for when the ball likely reaches its peak and then starts descending.
3. **x ≥ 2**: This indicates that after 2 seconds, the ball is still above ground, but it does not specify when it reaches ground height.
4. **2.5 < x < 5.5**: This suggests that after 2.5 seconds, the ball is still in the air (height above zero) until around 5.5 seconds.
Based on common projectile motion behavior, the ball will reach a maximum height shortly before it starts to descend and touchdown. If the ball is thrown from 48 feet, it might take it around 2.5 seconds to hit the peak and then descend.
Considering all options:
- **0 < x < 5.5** may be too broad.
- **0 ≤ x ≤ 2.5** likely covers the ascent phase only.
- **x ≥ 2** captures some of the descent phase.
- **2.5 < x < 5.5** is reasonable as it likely refers to the time the ball continues to descend after peak height(around 2.5) to landing.
Without a specific graph to analyze further, I recommend choosing **2.5 < x < 5.5** as this range likely corresponds to when the ball is falling after reaching its peak height, assuming it lands on the ground after 5.5 seconds.