Well, there several things that determine whether your answer will be accurate or not.
I'll start with air resistance. There are 2 major things that will
affect air resistance. The first is the size of the stone. The cross
sectional area of the stone will determine how much air resistance it
will experience. However, the size of the stone also determines how
heavy it is. Air resistance (discussed below) will be a problem for
your measurement if it gets anywhere near as big as the weight of the
rock. However, since the weight of the rock will be proportional to its
radius cubed, and the area of the rock to its radius squared, making
the rock bigger is good since it will make air resistance relatively
smaller than gravity.
The second part is the velocity of the stone. The cool thing about
air resistance is that it depends on how fast you are moving. That
makes sense if you think about it. You have to push through a lot more
air in the same time if you're moving faster. The velocity of the stone
depends on how tall the cliff is. If the cliff is very very very tall,
then the air resistance will eventually equal the force of gravity and
then your acceleration will be 0 instead of 9.81. That is called the
"terminal velocity" because it won't get any faster.
Then you mention the wind. Depending on how the wind is moving and
the shape of the cliff, the wind could actually flow up the cliff. That
could help slow the rock down a little bit if the wind is strong
enough.
So if your cliff isn't too high, and there isn't too much wind, and
you use a big rock, then you have a good way to tell the height of the
cliff.
Adam
(published on 10/22/2007)
