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)
Responses
0.4 second
0.4 second
4.0 seconds
4.0 seconds
1.6 seconds
1.6 seconds
40 seconds
Answers
GPT-4o mini
The time it takes for an object to fall under the influence of gravity can be derived from the formula for the distance an object falls, which is given by:
\[ d = \frac{1}{2} g t^2 \]
where:
- \( d \) is the distance (height of fall),
- \( g \) is the acceleration due to gravity (approximately \( 9.8 \, \text{m/s}^2 \)),
- \( t \) is the time in seconds.
In this scenario, both rocks are dropped from the same height (78.4 m), so they will both take the same amount of time to fall, regardless of their mass.
Since Rock 1 takes 4.0 seconds to fall, Rock 2 will also take the same time to fall, which is **4.0 seconds**.
Therefore, the answer is: **4.0 seconds**.
\[ d = \frac{1}{2} g t^2 \]
where:
- \( d \) is the distance (height of fall),
- \( g \) is the acceleration due to gravity (approximately \( 9.8 \, \text{m/s}^2 \)),
- \( t \) is the time in seconds.
In this scenario, both rocks are dropped from the same height (78.4 m), so they will both take the same amount of time to fall, regardless of their mass.
Since Rock 1 takes 4.0 seconds to fall, Rock 2 will also take the same time to fall, which is **4.0 seconds**.
Therefore, the answer is: **4.0 seconds**.