You are standing at the top of a deep, vertical cave and want to determine the depth of the cave. Unfortunately, all you have is a rock and a stopwatch. You drop the rock into the cave and measure the time that passes until you hear the rock hitting the floor of the cave far below. If the elapsed time is 8.0 s, how deep is the cave? (1) Sound travels at a constant speed of 340 m/s. (2) Consider both the time the rock undergoes free fall and the time it takes the sound to travel back up the cave. During the free-fall phase, the rock starts from rest, moves with a constant acceleration, and lands at the bottom of the cave. During the second period, sound travels at a constant velocity back up the cave.