Simple kinematics question -- dropping a stone down a well

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SUMMARY

A boy drops a 0.10 kg stone down a 150 m well and calculates the total time to hear the echo as 6 seconds. Using the kinematic equation v² = v² + 2ax, he determines the stone's final velocity at the bottom of the well, which takes 5.53 seconds to reach. The sound then travels back up the well at a speed of 343 m/s, taking an additional 0.437 seconds. The calculations confirm that the total time from drop to echo is accurate when rounded to significant figures.

PREREQUISITES
  • Understanding of kinematic equations, specifically v² = v² + 2ax
  • Knowledge of sound speed in air at 343 m/s
  • Basic algebra for solving equations
  • Familiarity with significant figures in calculations
NEXT STEPS
  • Study the derivation and application of kinematic equations in physics
  • Learn about the effects of air resistance on falling objects
  • Research the speed of sound in different mediums and conditions
  • Explore practical applications of echo location in various fields
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Students studying physics, educators teaching kinematics, and anyone interested in practical applications of motion and sound.

Mr Davis 97
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Homework Statement


[/B]
A boy drops a 0.10 kg stone down a 150 m well and listens for the echo. If the speed of sound is 343 degrees Celsius, the how long after the stone is dropped will the boy hear the echo?

Homework Equations



v = d/t

v2 = v2 + 2ax

The Attempt at a Solution


[/B]
What I did was use v2 = v2 + 2ax to find the velocity of the rock at the end of the well. Then I used v = at to find how long it takes to go from zero to that final velocity. Therefore, I found that the time it took to get to the end of the well was 5.53 s. Next I used t = d / v to find how long it took the sound to travel back, which is .437 s. Thus, adding these together, I got 6 s, rounded to sig figs. Is this answer correct?
 
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