Evaluate an approximate value of sqrt(2), using a sneaker and a stopwatch only.
Source: Mark Levi's "Why Cats Land On Their Feet?"
Use the sneaker to mark off two heights on the wall, one twice the other. Say 3 'feet' and 6 'feet'. Use the stopwatch to measure how long it takes the dropped sneaker to fall to the floor from each of these heights. The ratio of these times is the square root of 2.
This solution takes advantage of the fact that the distance an object falls (ignoring air resistance etc.) is proportional to the square of the time.
Assumption: we have a wall. It is also pretty hard to measure such short time intervals with a stopwatch so the accuracy is questionable.
A more accurate solution would be to let me use the stopwatch on my smartphone. Then I can quickly switch to a calculator app and give you 10 decimal digits.
Posted by Jer
on 2016-07-19 10:28:08