When an object is dropped from rest (and we ignore air resistance) the
time it takes to reach the ground depends only on the initial height
and the acceleration of the object. This acceleration is due to the
force of gravity, and is the same for all objects.
As any
object falls it usually encounters some degree of air resistance, which
is caused by the object's surface colliding with air molecules. The two
most common factors that determine the air resistance are the speed of
the object and its cross-sectional area. Greater speed causes greater
air resistance, and increased area increases air resistance as well. It
also depends on an object's shape. Parachutes have lots of air
resistance because of their big cross-sectional area and also their
cupped shapes. Cars, airplanes and boats are designed with smooth
shapes to reduce air (and water) resistance. In general, this air
resistance will mean that an object dropped from a certain height will
take longer to reach the ground.
It's not too clear what is
meant by "landing time" in this question, however. For an airplane, it
could mean the length of time between the time at which it starts
descending from its cruising altitude (usually 30,000 feet) until the
time it pulls into the gate at the airport, or the time it takes
between the first touch of the wheels on the runway and the time it
comes to rest. In both of these instances, air resistance is a big
factor (the free-fall gravity example above results in a very hard
crash-landing -- the "landing time" is very short, but it is not a
landing anyone would want to make).
In order to get down
from cruising altitude to the ground without hitting too hard, air
resistance plays a big role. When a plane drops from a high altitude to
a lower one, it naturally speeds up just like anything that is dropped.
It has to lose this energy somehow, and so the pilot will slow the
engines down, but usually this is not enough. The pilot will also
extend the landing gear and the flaps on the wings, both of which
increase the air resistance and slow the plane down. The more air
resistance there is, the faster the plane can slow down to make a safe
landing. On the runway, the pilot will even put the engines in reverse
(this is done with air diverters on the sides of the engines), blowing
air in front of the airplane, to slow the plane down even faster. If
there is too much air resistance, then the airplane will flutter like a
feather in the wind, or like a piece of paper. The reverse-engine trick
works on the ground because the wheels help keep the plane rolling
safely and stably while there is so much resistance to its motion.
You may notice birds doing the same kind of thing when they land. They
swoop down, and then just as they come in for a landing, they start
flapping their wings backwards, pushing air in front of them so they
come to a graceful stop and can grab onto a small branch. Air
resistance helps them slow down quickly and come in for a good landing.
(published on 10/22/2007)
