245 m well: time until the echo is heard

A stone is dropped from rest into a well 245 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 echo of the splash is heard.

Step-by-step

1. t₁ = √(2h/g) = √(2×245/10) = 7
   Time for the stone to free-fall to the bottom
2. t₂ = h/v_sound = 245/340 = 0.7206
   Time for the sound to travel back up to the top
3. t = t₁ + t₂ = 7.7206 s
   Total time = fall time + sound travel time

Why it works

The stone falls freely until it hits the water, and then the sound climbs the shaft at a constant speed; both stages cover the same depth, so the total time is their sum.

Common mistakes

• Averaging the stone's falling speed with the speed of sound.
• Assuming sound travels more slowly inside the well than 340 m/s.

Related

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