Final answer:
Using the kinematic equation for uniformly accelerated motion, with an acceleration due to gravity of -9.81 m/s² and a falling time of 4 seconds, the rock falls a distance of 78.48 meters.
Step-by-step explanation:
To determine how far a rock falls in 4 seconds with an acceleration due to gravity of -9.81 m/s², we can use the kinematic equation for uniformly accelerated motion: s = ut + ½at², where s is the displacement, u is the initial velocity, a is the acceleration, and t is the time. Assuming that the rock is dropped and therefore has an initial velocity of 0 m/s, the formula simplifies to s = ½at². Plugging in the values, s = ½(-9.81 m/s²)(4 s)², gives us s = ½(-9.81)(16), which equals -78.48 m. Because displacement refers to the change in position from an initial point, and since the rock is falling down, we take the absolute value to find the distance. The rock fell 78.48 meters.