# Terminal Velocity

From: DonRath@aol.com
Date: Tue Nov 17 1998 - 16:07:47 PST

reference to bullets that are fired straight up in the air.

If an object falls in a material that provides some resistance to its motion,
then it will have a terminal velocity. If it falls far enough, it will reach
this velocity, and maintain it for the remainder of its fall -- unless
something changes, as in the case of a skydiver who has reached terminal
velocity with arms outstretched, and then changes his/her profile. A ball
falling through air has a terminal velocity -- I've listed some values below.
Or if you want a more dramatic example, you can drop a marble in a bottle of
colorless Karo syrup -- you'll find that the marble will almost instantly stop
accelerating when dropped in the Karo, and will fall with a slow, steady,
speed -- and if you can find a steel ball of the same diameter as the marble,
you'll be able to see that its terminal velocity is notably higher than the
marble. An object falling in a vacuum (on the moon, for example) will not have
a terminal velocity, but will keep accelerating for as long as it is falling.

If you fired a bullet straight upwards on the moon, it would return to the
firing point with its initial velocity. But if you do this with air resistance
present, then this will not be true. If the bullet is fired high enough in the
air, it would have a long enough fall to be able to attain its terminal
velocity by the time it returned. Otherwise, its velocity would be something
less than this. But its velocity upon its return will always be something less
than the velocity with which it was fired upward. When air resistance is
present, the upward and downward parts of the trip are not symmetric.

The book Sport Science, by Peter Brancazio, contains these approximate
terminal velocities:
raindrop = 15 mi/hr
baseball = 95 mi/hr
golf ball = 90 mi/hr
ping pong ball = 20 mi/hr
On a web search I found a value of about 300 ft/sec (that's roughly 200
miles/hour) given as the terminal velocity of a .30 caliber bullet. I don't
know for sure that this is valid, but it seems reasonable, especially in light
of the values for the baseball and golf ball noted above.

I hope this helps.

Don Rathjen
donr@exploratorium.edu
OR
donrath@aol.com

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