125 m well: time until the echo is heard

A stone is dropped from rest into a well 125 m deep. Sound travels at 340 m/s in the air (g = 10 m/s²). Find the total time from releasing the stone until the sound of the splash is heard.

Step-by-step

1. t₁ = √(2h/g) = √(2×125/10) = 5
   Time for the stone to free-fall to the bottom
2. t₂ = h/v_sound = 125/340 = 0.3676
   Time for the sound to travel back up to the top
3. t = t₁ + t₂ = 5.3676 s
   Total time = fall time + sound travel time

Why it works

The stone falls freely while the splash sound travels back at a constant speed, and both cover the same 125 m, so the total time is the falling time plus the sound time.

Common mistakes

• Treating the whole interval as free fall at g and ignoring the sound.
• Making the sound cover two well depths, down and back up.

Related

echo-well vertical-throw free-fall-echo-well-20m