We decided to use this catapult as inspiration because it looks like it will shoot the ball consistently. Also, the amount of materials it uses is within our range.
This is a picture of our brainstorm/rough draft. It is very messy, but it helped us organize our thoughts in a visual way. This made completing our final catapult design plan very simple because we already had it figured out.
The first design of the catapult is not consistent. The pipes are not all the exact length, so they bend and change where the ball will land. Also, the bungee cords move, so the ball isn't launched consistently. It is also launching from 20-25 feet, so we need to make sure to not pull the arm back all the way.
Our final catapult can launch consistently. In order to do this, we made slight changes to our old catapult. First, we put screws in the top beam to keep the bungee cords in the same place. This helped the ball go exactly where we wanted it to go. We also pulled the catapult arm back to a measured length. By pulling it three inches from the ground, it is able to launch consistently.
Our final catapult can consistently launch to 23.5 feet and reaches a maximum height of 6.75 feet. The quadratic equation for our catapult's parabola is y=-.04(x-11.75)²+6.75. The target can be hit if it is placed directly on front of the catapult arm. Below is a picture of our data and the paper we used to solve the equation.
To make the catapult launch further, we can make the arm longer. This will make the starting point higher, which will launch the ball further.
The maximum height of the ball of 6.75 feet because this is the vertex. The vertex is the highest point on the parabola, so it can not get any higher. The maximum height occurred at the halfway point of the distance. The x value of the vertex is exactly half of the ending point's x value.