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

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Homework Help Overview

The problem involves calculating the depth of a well and the velocity of a rock dropped into it, with the splash being heard 20 seconds later. The context includes equations of motion and the speed of sound in air.

Discussion Character

  • Exploratory, Assumption checking, Problem interpretation

Approaches and Questions Raised

  • The original poster attempts to set up equations of motion but expresses uncertainty about the sufficiency of the information provided. Participants question the definition of the variable "t" in the context of the problem, seeking clarification on whether it refers to fall time, sound travel time, or total time.

Discussion Status

The discussion is ongoing, with participants exploring different interpretations of the time variable and suggesting a division of the problem into two distinct time intervals and equations. No consensus has been reached yet.

Contextual Notes

There is a noted concern about the potential lack of information necessary to solve the problem effectively.

Miri McPherson
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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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Which time are you indicating with "t?" Fall time? Or, travel time of the splash noise? Or, total time?
 
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.
 
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:
 

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