The time it takes for an object to fall can be calculated using the formula for free fall, which is based on the height of the fall and the acceleration due to gravity. The general equation for the distance fallen under gravity is:
\[ d = \frac{1}{2} g t^2 \]
where:
- \( d \) is the distance fallen (in meters),
- \( g \) is the acceleration due to gravity (approximately 9.8 m/s²),
- \( t \) is the time in seconds.
Given the distance \( d \) of 78.4 m, you can rearrange the formula to solve for time \( t \):
\[ t = \sqrt{\frac{2d}{g}} \]
You can apply this to both rocks:
Using rock 1's data (where \( d = 78.4 \) m and \( t = 4.0 \) s):
Calculate using the same height for rock 2:
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Calculate \( t \) for rock 1:
\[ t = 4.0 \text{ s} \Rightarrow 78.4 = \frac{1}{2} \times 9.8 \times (4.0)^2 \]
This verifies that the rock 1 calculation is consistent.
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Since rock 2 falls the same height (78.4 m) under the same conditions of gravity, it will also take the same time to fall, irrespective of its mass.
Therefore, rock 2 will also take 4.0 seconds to fall.
The final answer is: 4.0 seconds.
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