Stone dropped into a 20 m well: echo time

A stone is dropped from rest into a well 20 m deep. Sound travels at 340 m/s in air (g = 10). Find the total time from releasing the stone until the splash is heard.

Step-by-step

1. t₁ = √(2h/g) = √(2×20/10) = 2
   Time for the stone to free-fall to the bottom
2. t₂ = h/v_sound = 20/340 = 0.0588
   Time for the sound to travel back up to the top
3. t = t₁ + t₂ = 2.0588 s
   Total time = fall time + sound travel time

Why it works

Two stages share the same distance: the stone falls freely downwards and the splash sound travels back up at a constant speed, so the total time is the sum of a fall time and a sound time.

Common mistakes

• Treating the whole trip as free fall at g.
• Using 2 × 20 m for the sound because the sound goes down and up.

Related

echo-well meeting-problem free-fall-echo-well-180m