Stone dropped into an 80 m well: echo time

A stone is dropped from rest into a well 80 m deep. Sound travels at 320 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) = √(2×80/10) = 4
   Time for the stone to free-fall to the bottom
2. t₂ = h/v_sound = 80/320 = 0.25
   Time for the sound to travel back up to the top
3. t = t₁ + t₂ = 4.25 s
   Total time = fall time + sound travel time

Why it works

Downwards the stone is in free fall, so the depth fixes that time; upwards the sound moves at a constant 320 m/s over the same 80 m, and the two times add.

Common mistakes

• Stopping the clock when the stone hits the water.
• Adding the two speeds instead of the two times.

Related

echo-well vertical-throw free-fall-echo-well-500m