1951 AHSME Problems/Problem 39
Problem
A stone is dropped into a well and the report of the stone striking the bottom is heard seconds after it is dropped. Assume that the stone falls
feet in t seconds and that the velocity of sound is
feet per second. The depth of the well is:
Solution
Let be the depth of the well in feet, let
be the number of seconds the rock took to fall to the bottom of the well, and let
be the number of seconds the sound took to travel back up the well. We know
. Now we can solve
for
:
And similarly
:
So
. If we let
, this becomes a quadratic.
We know
is the positive square root of
, so we can replace the
with a
.
Then
, and the answer is
.
See Also
1951 AHSC (Problems • Answer Key • Resources) | ||
Preceded by Problem 38 |
Followed by Problem 40 | |
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