1) What are routinely used to determine atmospheric wind speed by tracking the movement of winds?
A time sequence of satellite images.

2a) If a cloud caught the "jet stream express" and traveled 100 miles in 20 minutes, how fast did it go?
5 miles per minute

2b) What was its speed in miles per hour?
300 mph!

3) What is an advantage of deriving wind speeds (and direction) from satellite images?
Recall that about 70% of the earth is covered by water where conventional weather observations are not possible. While it's true that buoys and ships send in weather observations they simply can't contribute anywhere near the coverage offered by satellites. The accuracy of weather forecasts improved dramatically during the 1990's due to the addition of satellite derived winds in forecast models. As one can imagine, this is especially crucial to the timing and location of where a hurricane makes landfall.

4) In tracking clouds we have additional problems besides not knowing the actual path of the cloud. What are some of these additional problems?
A cloud's shape changes with time. It may become distorted or even dissipate. The cloud feature in one image will most likely be different in another image at a later time. Therefore, tracking clouds can be quite difficult.