The Catapult Challenge

# Materials:

• Catapult
• Rubber bands
• Various types of projectiles
• Tablet with regression app installed
• Tape Measure

# Instructions:

In this experiment, you will be using a rubber band catapult to develop a learning function to predict the distance a Ping-Pong ball will fly when launched.  Your goal is to be able to hit a target a certain distance away from your catapult.  To do this, you need to be able to “dial in” the settings of your catapult.  In essence, you need to answer the question: “What settings should I use to achieve the target?” Begin by familiarizing yourself with the catapult.  Understand how to mount it, determine what factors you can vary, observe the trajectory of the ball (how far does it fly?), determine how best to measure the length of flight, and decide roles for each of your team members.

Once you are familiar with the catapult, do some trial launches to see what range of distance and heights you can achieve.  Note that you have the option of using one or two rubber bands to change the stiffness of the catapult.  Decide what general settings you want to use, and prepare to collect data for your regression.

Some of the settings you can vary are:

• # of rubber bands
• Launch angle (“Stop angle”)
• Type of ball
• Pull-back angle

# Data Collection and Analysis:

Before collecting data, make sure you have a consistent method for measuring distance flown and recording the results.  Start collecting data by recording the distances of your launches. Your first launch should be retracted to a pull-back angle of 20 degrees, and then each subsequent launch 10 degrees further (e.g. 20, 30, 40, 50, 60). Record about ten distances and write them down in a table like the one below.  Repeat some of your trials to make sure your launching method is consistent, and your measurement error is not a large factor in your data.  You can also try some intermediate pull back angles to fill out your data set.

Once you have your data points, open the Linear Regression app on your tablet. Input the Pull-back angles as your “X” data points and the distance as your “Y”.  Find the equation that describes the relationship between pull back angle and distance.  Look at the graph of your data with the regression line; is the equation a good predictor of the launch distance?  Why or why not?

Write down the equation it gives you. This is your model to predict the distance the catapult will launch the ping-pong ball for this set-up for a given pull-back angle. Also record your “R2” value.

 Pull Back Angle(degrees) Distance 20 30 40 50 60 70 80 90 100 110

 Pull Back Angle(degrees) Distance 20 30 40 50 60 70 80 90 100 110 Pull Back Angle(degrees) Distance 20 30 40 50 60 70 80 90 100 110

Does this R2 value seem to be low or high (between 0-1)? What is the meaning of this?  Move onto a new catapult set-up once you are satisfied and record 10 more data points to input into the app. You will create a new linear model for each set of data so be sure to write down each equation and test its accuracy. We will convene at the end to test whose model is the most accurate!