What equation shows a freely falling rock drops a distance of 80m when it falls from rest for 4s?

The correct equation demonstrates that the distance traveled by a freely falling object (like the rock in this scenario) can be calculated using the formula (s = \frac{1}{2} g t^2), where (s) is the distance, (g) is the acceleration due to gravity (approximately (10 , \text{m/s}^2) in the context of this problem), and (t) is the time in seconds.

In this case, the rock falls from rest for (4) seconds. Plugging the values into the equation yields:

[ s = \frac{1}{2} \cdot 10 , \text{m/s}^2 \cdot (4 , \text{s})^2 ]

Calculating this step-by-step:

1. ( (4 , \text{s})^2 = 16 , \text{s}^2 )
2. ( 10 , \text{m/s}^2 \cdot 16 , \text{s}^2 = 160 , \text{m} )
3. ( \frac{1}{2} \cdot