The Flight
Projectile Range Activity

To Bounce or Not to Bounce
Projectile Range Activity
Graphing Calculator Activity

Overview of Lesson

Students will use a mechanical pitching machine to test predictions about the range of a projectile.

Goal

Students will apply their understanding of two-dimensional kinematics, gravity, air drag and the Magnus force to make meaningful predictions about the flight of a ball and then test those predictions using a mechanical pitching machine.

Objectives

• The students will apply the equations of kinematics to a two-dimensional motion situation.

• The students will apply Newton's laws of motion to an object subject to multiple forces.

• The students will be able to estimate a baseball's range for several different sets of starting conditions.

• The students will predict the effect of changing variables.

• The students will discuss the limitations of their predictions and experimentation.

Ohio Academic Content Standards

Materials

• Pitching machine
  Note: Most schools should have access to a pitching machine through their PE or athletic departments. The type needed has two spinning rubber wheels whose speed can be controlled independently. They are commonly referred to as JUGS machines because many are made by the JUGS Company: http://www.thejugscompany.com.

• Several baseballs and an optional lacrosse or other smooth ball of a similar size and weight

• Extension cords

• A large outdoor field area

• Assorted bright colored flags or cones to mark landing spots

• Protractor for measuring angles

• Long (50-100 m) measuring tape

• Calculators

• Sports radar gun to measure ball speeds (optional, but recommended)

Procedure

1. Before beginning the activity with the class, spend some time learning to safely use the pitching machine. Make some practice "launches" to see how much space will be needed and to get an idea of the velocity settings you will use.

2. Explain to students that this activity will have them making predictions about the flight of a baseball and then testing them using a mechanical pitching machine.

3. Orient the students to the workings of the pitching machine and discuss with them the safety precautions needed. (The machine should be operated only by a qualified adult and all manufacturers' safety precautions should be observed.)

4. Before taking the class outside with the machine, have them make some predictions.

   a. With a given starting velocity (measured previously, about 70 mph) and a launch angle of 45 degrees, how far should a ball fly? This is easily calculated using the following kinematics equation:

   
   

   b. If we add in the variable of air drag, how might this affect the range of the ball?

   c. If we add in the variables of air drag and topspin, how will the range of the ball be affected?

   d. If we add backspin rather than topspin, what will be the result?

   e. Will the optimum launch angle still be 45 degrees when the other variables are introduced? How might it change?

   Predictions (b.) through (e.) are best done as educated estimates rather than numerical calculations. Have students do more than just guess at a number; ask them to justify their predictions based on their understanding of air drag and the Magnus force. Have students look back to the pitch trajectory graphs that they made previously (lesson plan on page 23) to help them make the predictions.

   f. What would happen to the range if the baseball were replaced by a smooth ball of similar size and weight?

5. Once predictions have been made, it's time to go outside and do some testing! Position students in a safe vantage point. Begin by setting the wheels of the pitching machine to the same speed, allowing for as little ball spin as possible, and set the launch angle to 45 degrees. Launch a few balls, marking the spots where they land with cones or flags. Measure the range using the tape measure. Compare to the value in prediction (b.). Remind students that there is no way to test their calculated prediction (a.) because the range equation they used neglects air drag.

6. Test out the effect of adding topspin and backspin by adjusting the rotational velocity of the wheels of the pitching machine. If the top wheel moves faster, it will impart topspin on the ball and the opposite is naturally true to get backspin. It is a good idea to use a sports radar gun to make sure that the launch velocity is consistent each time. Making adjustments to the rotational velocities of the wheels will affect the overall velocity of the ball as it leaves the machine. If care is taken to keep the velocity constant, you should observe that the ball launched with backspin will fly farther.

7. Test prediction (e.) by leaving the rotational velocity of the wheels on the machine constant and varying the launch angle until you find the angle that sends the ball the farthest.

8. Test prediction (f.) by substituting a lacrosse ball in the machine.

9. Finish the experiment by asking students to use the observations they have made to predict what combination of variables would result in the longest home-run balls. If different predictions are made, then test them out and see which is better. Studies have shown that a ball hit as hard as possible, with a lot of backspin, at an angle of about 33 degrees has the best chance to fly out of the park.

10. A follow-up discussion should include looking at the ways in which a ball hit by a batter during a baseball game is different than one thrown by a mechanical pitching machine. You can note that a batted ball has much higher velocity (well over 100 mph) and that other variables such as wind direction and sideways spins can also play a major role.

Evaluation

The evaluation for this activity is informal and based upon the written predictions the students make. The relative accuracy of the predictions made, and the justifications supporting their predictions, are used to gauge the students' understanding of the concepts involved. The activity may also be written up in a more traditional science lab format. See Appendix C for evaluation rubric.

Note

Tennis ball machines may work for this activity, as may a ball launcher made from some kind of air cannon. The key idea is that you need a way to launch a ball with consistent velocity, plus you must also be able to impart spin as well as change the launch angle.