Re: how do they measure the speed of a fastball?

The speed of a fastball (or a tennis serve) is measured by the same device that
measures the speed of a automobile.  It is called a radar gun.  The simple idea
is that a signal is sent out, hits the moving object and some of the signal
bounces off the object and returns to the gun's receiver and some hits other
stuff and may return to the gun as well.

If the part of the signal that hits the moving object can be separated from the
rest of the signal coming from anything else then the speed of the object can be
determined.  Usually this is done by looking at the frequency shift of the
return signal (Doppler Shift). But it used to be done by collecting multiple
signals at regular intervals in time.  The signal returns at a time proportional
to the distance traveled.  The processor in the gun can take two or more data
points and compute the difference in distance between the two or more points. 
Knowing the time between signal sendings the speed is calculated by
Distance difference / signal period.  The doppler shift method typically is more 
accurate but requires more expensive equipment and is has built in corrections
for motion that is not purely toward or away from the gun.  The second method
comes from World War II radar or sonar technology and works very well for long
distances (and metal objects) or inline with the motion of the object.

Tom "Slow Ball" Cull