All Fermi answers
Fermi #47 · Question 2

If you dropped a cannonball off a boat over the Mariana Trench, how long would it take to reach the bottom?

Explore the official answer and the simple reasoning behind this Fermi estimate.

2QUESTION 2 OF 3

Answer & explanation

The official answer, with Fermi’s reasoning step by step.

Answer & explanation

Official answer

2,500

seconds

How to estimate it

Fermi’s official “Napkin math”

The Mariana Trench is about 11 kilometers deep, the lowest point in the ocean. How fast does a heavy iron ball sink? Maybe 4 or 5 meters a second.

Trench depth
11,000 m
Sink speed
~4.5 m/s
11,000 ÷ 4.5
≈ 2,500 sec

Rounded assumptions may give a slightly different estimate. The official answer above is the game’s reference value.

Source calculation & reference
Trench depth
≈ 11,000 m
Terminal velocity in water
÷ 4.4 m/s
11,000 ÷ 4.4
≈ 2,500 (~42 min)

Reference cited by Fermi: NOAA Challenger Deep depth · drag-equation estimate for a solid iron sphere

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