CalcElfCalcElf › Stone in a well: time until you hear the spl
Stone in a well: time until you hear the spl
A well is 45 m deep. A stone is dropped from the top and sound travels at 340 m/s. Find the time from release until the splash is heard.
Answer
Total time ≈ 3.1324 s (fall 3 s + sound 0.1324 s)
Step-by-step
- t₁ = √(2h/g) = √(2×45/10) = 3Time for the stone to free-fall to the bottom
- t₂ = h/v_sound = 45/340 = 0.1324Time for the sound to travel back up to the top
- t = t₁ + t₂ = 3.1324 sTotal time = fall time + sound travel time
Why it works
There are two stages: the stone falls (free fall) and then the sound travels back up at constant speed. Add the two times.
Common mistakes
- Using the sound speed for the falling stage.
- Forgetting to add the return time of the sound.