Question
Rock
1
Rock
2
Mass (kg)
2.5
25
Height of Fall (m)
78.4
78.4
Time to Fall (s)
4.0
?
Based on this data, how many seconds will it take rock 2 to fall?
(1 point)
• 0.4 second
• 1.6 seconds
40 seconds
• 4.0 seconds
1
Rock
2
Mass (kg)
2.5
25
Height of Fall (m)
78.4
78.4
Time to Fall (s)
4.0
?
Based on this data, how many seconds will it take rock 2 to fall?
(1 point)
• 0.4 second
• 1.6 seconds
40 seconds
• 4.0 seconds
Answers
GPT-4o mini
To determine the time it will take for rock 2 to fall, we can use the formula for the time of free fall under the influence of gravity:
\[
t = \sqrt{\frac{2h}{g}}
\]
where:
- \( t \) is the time in seconds,
- \( h \) is the height in meters,
- \( g \) is the acceleration due to gravity (approximately \( 9.81 \, \text{m/s}^2 \)).
Given that both rocks are dropped from the same height of 78.4 meters, we can calculate the time for rock 2 as follows:
\[
t = \sqrt{\frac{2 \times 78.4}{9.81}}
\]
Calculating:
\[
t = \sqrt{\frac{156.8}{9.81}} \approx \sqrt{15.98} \approx 4.0 \text{ seconds}
\]
Since the heights of both rocks are the same and they are both dropped (assuming air resistance is negligible), the time it will take rock 2 to fall is:
**4.0 seconds**.
So the answer is:
- **4.0 seconds**
\[
t = \sqrt{\frac{2h}{g}}
\]
where:
- \( t \) is the time in seconds,
- \( h \) is the height in meters,
- \( g \) is the acceleration due to gravity (approximately \( 9.81 \, \text{m/s}^2 \)).
Given that both rocks are dropped from the same height of 78.4 meters, we can calculate the time for rock 2 as follows:
\[
t = \sqrt{\frac{2 \times 78.4}{9.81}}
\]
Calculating:
\[
t = \sqrt{\frac{156.8}{9.81}} \approx \sqrt{15.98} \approx 4.0 \text{ seconds}
\]
Since the heights of both rocks are the same and they are both dropped (assuming air resistance is negligible), the time it will take rock 2 to fall is:
**4.0 seconds**.
So the answer is:
- **4.0 seconds**