The Arizona STEM Acceleration Project
Bounce Adventures - A Projectile Motion Game
Bounce Adventures
A 7-12 grade STEM lesson
David Wirth
May 2024
Notes for teachers
The students in this lab activity will play a competitive game with a small bouncy ball. The students will analyze the motion of the ball and apply projectile motion concepts. This activity requires very little equipment and can be completed in a few class periods.
This lesson comes at the end of a unit on projectile motion and students should also be familiar with conservation of energy concepts.
List of Materials
Standards
Plus HS+Phy.P3U1.3 Develop a mathematical model, using Newton’s laws, to predict the motion of an object or system in two dimensions (projectile and circular motion).
Standards
Standard 5. Computational Thinker - Students develop and employ strategies for understanding and solving problems in ways that leverage the power of technological methods to develop and test solutions.
RFR.AF.3 Interpret key features of graphs and tables for a function that models a relationship between two quantities in terms of the quantities.
Objectives:
The students will determine the horizontal and vertical velocities of a ball traveling as a projectile. In addition, the students will answer projectile motion type questions related to the motion of the ball.
Agenda
Day 1
10 minutes - Intro
20 minutes - Students play the game.
20 minutes - Students solve problems and answer questions related to the game.
Day 2
25 minutes - finish solving problems and answering questions related to the lab.
25 minutes - Have students present their whiteboards to each other.
**Depending on how students attack this problem it could take a few more days.
Intro/Driving Question/Opening
We are going to play a competitive game involving a bouncy ball and tables which are spaced equally apart. The diagram below shows four tables which are spaced a few feet apart. The goal is to bounce a ball so that it lands on each table exactly once. See how many times it takes you to get it.
After playing the game - Discussion.
What strategy worked the best? Why?
How does the strategy you used support what we learned about projectile motion?
Did the ball lose energy during this game? How do you know? Where did it go?
Hands-on Activity Instructions
Play the game again. Observe and collect data and answer the following questions. Write your answers on a whiteboard which you will present to the class.
For a successful throw (3 - 4 bounces):
1.) Find the horizontal velocity of the ball.
2.) Did the horizontal velocity of the ball change?
A.) If so, why?
3.) Find the vertical velocity of the ball upon
leaving the table.
4.) About what percent of the energy was lost
from one bounce to the next?
Give data, graphs and observations to support your claims.
Common Solutions
1.) Horizontal Velocity of ball:
Solution A: Kinematics: determine the time needed for the ball to travel a measured horizontal distance.
3.) Vertical Velocity of ball:
Solution A: Kinematic equations.
Determine the vertical height (Δy)from the table top to the top of the path.
Common Solutions (continued)
4.) About what percent of the energy was lost from the initial bounce to the final bounce?
Potential Energy at Point A = mghA
Potential Energy at Point B = mghB
% Energy Lost = (mghB - mghA)/mghA)x100%
A
B
Video Analysis Solution
The graph above shows a constant horizontal velocity of 2.55 m/s before the bounce and a constant horizontal velocity of 2.29 m/s after the bounce
Video Analysis, Vertical
The vertical acceleration shows about -10 m/s2 before the bounce and -8.7 m/s2 after the bounce. The difference is likely due to a distortion of the ball in the video. It’s hard to determine the center of the ball.
Video Analysis - loss of energy loss during bounce.
First Bounce Height = 1.089 m - 0.289 m = 0.8 m Initial PE = mgh = (0.46 kg)(10 N/kg)(0.8 m) = 3.7 J
Second Bounce Height = 0.863 m - 0.289 m = 0.57 m Final PE = mgh = (0.46 kg)(10 N/Kg)(0.57 m) = 2.6 J
Initial KE = (½)(0.046 kg)(2.55 m/s)2 = 0.15 J �Final KE = (½)(0.046 kg)(2.29 m/s)2 = 0.12 J % Energy Lost = ((2.72 J - 3.85 J)/3.85 J) = - 29%
Assessment
An airplane traveling at 60 m/s drops a survival package to the survivors on a deserted island as shown above.
A.) If package is dropped when D = 360 m, determine how long it will take the package to hit the island.
B.) Determine, h, the altitude of the airplane.
C.) What is the horizontal and vertical velocity of the package at t = 2s.
D.) What happens to the energy of the package when it hits the island?
Differentiation
Remediation
Extension/Enrichment
Have students play the game with varying degrees of separation of the tables and have them find corresponding relationships.
Have students use the Video Analysis App or Tracker to solve for relationships.
Have students use the data from Video Analysis to find the normal force on the ball.