How deep is the well?

In one episode of the television series Time Team, the indefatigable archaeologists want to measure the depth of a mediaeval well. They drop something into it and time its fall, which takes an amazingly long six seconds. You hear it clattering its way down for ages. They come dangerously close to calculating the depth using Newton’s laws of motion, but cop out at the last moment and use three very long tape measures joined together instead.

The formula they very nearly state is

$s=\frac{1}{2}gt^{2}$

where s is the distance travelled under gravity, falling from rest, and g is the acceleration due to gravity. It applies when air resistance can be ignored. This formula was discovered experimentally by Galileo Galilei and later generalized by Isaac Newton to describe motion under the influence of any force.

Taking $g= 10 m s^{-2}$how deep is the well?

You’ve got three days to do it.

Ref: Prof Ian Stewart’s Cabinet of Mathematical Curiosities.

More treasures coming from Prof Stewart’s cabinet for us later,

Nalin Pithwa

One Comment

1. Anubhav Clancy Singh
Posted July 11, 2016 at 10:52 am | Permalink | Reply

It might be more than a month overdue, but better late than never, right?
S=(1/2)*10*(6^2), which gives S to be 180m.

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