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©2009 by L. Lagerstrom
Calculating the Depth of a Well
• For an overview of this example, see the associated
video clip
• The situation
• Deriving an equation for the depth
• Using the roots function to find the depth
©2009 by L. Lagerstrom
The Situation
Imagine that we have found an old well and want to figure out how
deep it is. We have a stopwatch, so we decide to drop a rock down
the well and time how long it takes until we hear the splash. We
need to know if we can find the depth from this information.
First, let d = the depth of the well and t = the time until we hear the
splash. We know that the rock falls under the influence of gravity and
that its initial velocity is 0 (i.e., we don't throw it downward, but just
release it at the edge of the well). So the distance traveled by the
rock from the top of the well to the water level is:
where g = acceleration due to gravity (9.8 m/s
2
) and t
f
= the time of
fall for the rock.
2
2
1
f
gt
d
=
©2009 by L. Lagerstrom
The Situation, cont.
We have noted we can calculate the depth of the well by:
There's a problem, however. We don't know the time of fall t
f
. The
time we measured on our stopwatch is the time of fall plus the time
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 Spring '10
 Lagerstrom
 Equations, Quadratic equation, Elementary algebra, L. Lagerstrom

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