To find out how long it takes Rock 2 to fall, we can use the formula for the time of fall under gravity, which is a function of height:
\[ t = \sqrt{\frac{2h}{g}} \]
where:
- \( t \) is the time in seconds,
- \( h \) is the height in meters (78.4 m in this case),
- \( g \) is the acceleration due to gravity (approximately \( 9.81 , \text{m/s}^2 \)).
For rock 1, the time to fall is given as 4 seconds. We can verify that this time is consistent with the height of fall:
\[ t = \sqrt{\frac{2 \times 78.4, \text{m}}{9.81, \text{m/s}^2}} \approx 4 \text{ seconds} \]
Given that both rocks are falling from the same height and in the same gravitational field, the time it takes for Rock 2 to fall will also be 4 seconds since the time of fall is independent of mass for objects in free fall.
Therefore, the time it takes Rock 2 to fall is:
4.0 seconds.