Mathematical Model

For our mathematical model, we tested different weights in our box, and tested to see how it would change how far our tennis ball threw out of our trebuchet. With our base amount of weight in the box, it was capable of throwing 486 inches (or 40.5 feet.) Then, we added different amounts of weight (in grams) to our box. We found that for every 500 grams that we added, it averaged an amount of about 40.5 (3.375 feet) inches extra per throw. So, we can estimate how far our trebuchet can throw based on how much weight we have added into our trebuchet. Our model would then be f(x) = 486 + 40.5x. This means that it will default throw that original 486 inches, and for every 500 grams that we add (1 extra x), it will throw that additional 40.5 inches.