To determine the time it will take for Rock 2 to fall from a height of 78.4 meters, we can use the physics of free fall, which is independent of mass. The time of free fall for an object under the influence of gravity can be calculated using the formula:
\[ d = \frac{1}{2}gt^2 \]
where:
- \(d\) is the distance fallen (78.4 m),
- \(g\) is the acceleration due to gravity (approximately \(9.81 , \text{m/s}^2\)),
- \(t\) is the time in seconds.
We can rearrange the formula to solve for \(t\):
\[ t = \sqrt{\frac{2d}{g}} \]
Substituting in the values:
\[ t = \sqrt{\frac{2 \times 78.4 , \text{m}}{9.81 , \text{m/s}^2}} \]
Calculating the right-hand side:
\[ t = \sqrt{\frac{156.8}{9.81}} \approx \sqrt{15.98} \approx 4.0 , \text{s} \]
Since Rock 1 takes 4 seconds to fall 78.4 meters, Rock 2, which has a different mass but falls from the same height, will also take approximately 4 seconds to reach the ground.
Thus, the time it will take Rock 2 to fall is also about 4 seconds.