1. Create a catapult that will be able to launch a bird
(tennis ball) into the air.
2. Once built, create a real life situation where you would have to knock down a tower filled with pigs 30 feet away (jenga blocks or toilet paper rolls piled up).
a. Launch your bird into the air and record or take pictures of the situation where the bird does not totally knock down the tower.
b. Launch your bird into the air and record or take pictures the situation where the bird does knock down the tower. If your catapult is not able to reach the 30 feet, move your catapult closer or further away from the pile in order to knock it over. Record the distance.
3. With the photos or video, create two quadratic equations with the placement of the catapult set at the origin.
4. Determine the zeros of the two quadratic functions – what does the zeros dictate?
5. Based on the quadratic equations created, what is the maximum?
To create a catapult that can launch a bird (tennis ball) into the air, you will need the following materials:
1. Base: Start with a sturdy base like a wooden board or a solid platform.
2. Arm: Create an arm using a long, thin wooden or metal rod. This arm should be able to pivot at one end on the base.
3. Bucket or Cup: Attach a bucket or cup at the free end of the arm. This will hold the tennis ball.
4. Tensioning Mechanism: Add a tensioning mechanism to create the force needed to launch the bird. This can be achieved by using rubber bands or springs. The tension should be adjustable to control the launch distance.
Once you have built the catapult, you can proceed with the real-life situation of knocking down a tower filled with pigs 30 feet away using jenga blocks or toilet paper rolls piled up.
a. Launch your bird into the air and record or take pictures of the situation where the bird does not totally knock down the tower. This will help you analyze the trajectory of the bird and make adjustments if needed to improve accuracy.
b. Launch your bird into the air and record or take pictures of the situation where the bird does knock down the tower. If your catapult is not able to reach the 30 feet, you can move your catapult closer or further away from the pile to adjust the launch distance. Record the distance achieved.
With the photos or video you have captured, you can create two quadratic equations with the placement of the catapult set at the origin (0,0). These equations will represent the trajectory of the launched bird.
To create quadratic equations, you will need data points from the recorded launch situations. Using these data points, you can apply the quadratic equation formula: y = ax^2 + bx + c. By substituting the x and y values from the data points into the equation, you can solve for the unknown coefficients a, b, and c.
Once you have the quadratic equations, you can determine the zeros of the two equations. The zeros represent the x-values where the y-values (trajectory) are equal to zero. In the context of knocking down the tower, the zeros can indicate the points at which the bird hits the tower.
Based on the quadratic equations created, you can also determine the maximum value. Since the quadratic function represents a parabola, the maximum value represents the highest point or peak of the parabolic trajectory. In the context of the catapult, this maximum point can represent the highest point reached by the bird during its flight.