Question Use the table of data for two falling rocks to answer the 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 40 seconds 40 seconds 0.4 second 0.4 second 4.0 seconds 4.0 seconds 1.6 seconds 1.6 seconds Skip to navigation

1 answer

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.