During the Civil War, air balloons were used for reconnaissance as well as for attacking enemy operations on the ground. Bricks and anything else they could think of were dropped on potential targets. As "civilization" progressed, airplanes replaced the air balloons. Bricks and cannon balls were dropped from the sky. At first, there were very few airplanes. Time passed. All sides had airplanes and guns were used plane to plane. Fortunately as the case may be, those who were shooting often shot off their own propellers before managing to shoot the enemy planes.

All of the above efforts at improving military prowess involved the force of gravity. Dropping bricks and cannon balls without extra force constitutes FREE FALL. Throwing bricks or shooting bullets, however, involves extra forces as well as free fall. Even with simple objective like dropping water balloons from a rooftop, timing is of the utmost importance in acheiving the target.

This data is from a free fall experiment. THe units of measure are seconds for time, t, and feet for height, h. If a relationship exists between time and height, acheiving the target is predictable rather than random. See what you can do.

Time t Height h

1 16

2 64

3 144

4 256 (graph data)

5 400

6 576

7 784

8 1024

9 1296

10 1600

-Find algebraic equation that relates to t and h and works for all the data given. THis is the mathematical model that would help you predict free fall.

-Describe a situation under which your model of free fall would not apply

-Using your mathematical midel, predict how long it would take for a water balloon to fall 20 feet (about 2 floors)

-A water balloon is held out a window at a height of 15 feet above the ground and a pedestrian is approaching but not yet underneath a location directly below the balloon. Draw a sketch. What information do you need to acheive your target?

-When dropping water balloons using free fall, what would make the balloons drop faster?