Final answer:
To find the depth of the water in a well, we consider the time for the rock to fall and the time for the sound to travel back. Using the acceleration due to gravity and the speed of sound, we can determine that the correct depth is approximately 96.54 meters.
Step-by-step explanation:
To calculate the distance below the top of the well to the surface of the water, we need to account for two main phases of the event: the time it takes for the rock to drop and hit the water, and the time it takes for the sound of the splash to travel back up the well to us.
Let's use the formula for the distance covered under constant acceleration due to gravity, which is d = (1/2) * g * t2 where g is the acceleration due to gravity (9.8 m/s2) and t is the time in seconds. We also use the formula speed = distance/time to calculate the distance that sound covers when it travels back up the well at a speed of 334 m/s.
- Let t1 be the time it takes for the rock to hit the water.
- Let t2= 5.72 - t1 be the time it takes for the sound to reach the listener after the splash.
Thus, the distance to the water, d, can be expressed as:
d = (1/2) * g * t12 = 334 * t2
By solving these two equations, we find that t1 is approximately 2.57 seconds, and d is approximately 96.54 meters below the top of the well. Therefore, the correct answer is c) 96.54 m.