Calculating the Depth of a Well and Velocity of a Rock Using Equations of Motion

In summary, the conversation discusses the depth of a well and the velocity of a rock that is dropped into it. It also includes equations for calculating velocity and the variables of sound and gravity. The question is raised about which time is being referred to in the equations, specifically in relation to the sound of the splash being heard.
  • #1
Miri McPherson
2
0
1. A rock is dropped into a well of an unknown depth. 20 seconds after the rock is dropped the splash is heard at the top of the well. What is the depth of the well? What is the velocity of the rock when it reached the bottom?2. X= Xo + Vo(t) + 0.5(a)(t^2)
V= Vo + a(t)
(V^2)= (Vo^2) + 2a(X-Xo)
Velocity of sound in air=343 m/s
Acceleration of gravity= -9.80 m/(s^2)

3. 0= Xo + 0.5(-9.80)(20-t of sound)
X= 343(t)
I feel like there isn't enough information, but I'm not sure. Any help would be greatly appreciated.
 
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  • #2
Which time are you indicating with "t?" Fall time? Or, travel time of the splash noise? Or, total time?
 
  • #3
Bystander said:
Which time are you indicating with "t?" Fall time? Or, travel time of the splash noise? Or, total time?
The time is from the time that the rock was dropped until the sound was heard.
 
  • #4
Miri McPherson said:
The time is from the time that the rock was dropped until the sound was heard.

Welcome to the PF.

Divide it up into two times and two equations. Can you take a cut at doing that? :smile:
 

1. What is the purpose of finding the depth of a well?

The depth of a well is important for various reasons. It helps determine the total volume of water that can be extracted from the well, the quality of the water, and the type of equipment needed for extraction.

2. How is the depth of a well measured?

The depth of a well is typically measured using a measuring tape or a special instrument called a sounding tape. The tape is lowered into the well until it reaches the bottom and the measurement is recorded.

3. What factors can affect the depth of a well?

The depth of a well can be influenced by various factors such as geological formations, topography, and the depth of the water table. It can also be affected by human activities such as drilling techniques and extraction methods.

4. What are the potential risks of not accurately determining the depth of a well?

Not knowing the exact depth of a well can lead to various problems. It can result in over-extraction of water, which can deplete the water supply or cause the well to run dry. It can also lead to the installation of incorrect equipment, leading to maintenance issues and potential contamination of the water source.

5. How often should the depth of a well be measured?

The depth of a well should be measured during the initial drilling and construction process. It is also recommended to measure the depth periodically, especially after any major changes in the surrounding area or if there are any changes in the water supply or quality.

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