Projectile motion refers to the motion of an object projected into the air at any angle and where the only force acting upon it is the force of gravity.  A few examples of this include a soccer ball being kicked, a baseball being thrown, or an athlete long jumping. Even fireworks and water fountains are examples of projectile motion. In this
lesson you will learn the fundamentals of projectile motion. You will be given examples and interesting facts and learn the equations necessary for calculating the height, range and time in air of projectiles when the angle of launch is known.  As a result of this internet activity, you will then be able to build your own launcher and pre calculate the landing point of a golf ball (your projectile).  You will then test your launcher for accuracy and re-engineer if necessary.

You and other members of your group should visit each of the internet sites listed below.  Read the information found there and perform any required activities.  At sites in which there are interactive applets, experiment with such aspects of projectile motion as velocity, angle of launch, wind (drag) and any other variables located there.  As a result of visiting these sites, you should be able to answer the following questions about projectile motion.
 
 

1.   (a)  Describe the vertical motion of a projectile launched at an angle.
      (b) Describe the horizontal motion of a projectile launched at an angle.
      (c) What effect does the vertical motion have on the horizontal motion of the projectile?
      (d) Why is the path of a projectile parabolic in shape?

Internet Resources:

 http://www.glenbrook.k12.il.us/gbssci/phys/Class/vectors/u3l2b.html
 http://www.glenbrook.k12.il.us/gbssci/phys/mmedia/vectors/nhlp.html
 http://webphysics.ph.msstate.edu/ip/projectile.html

2.   (a)  How does the initial velocity of a projectile effect the range when all other factors are constant?
      (b) How does the angle of launch effect the range when all other factors are constant?
      (c) At what angle is maximum range achieved in the absence of air resistance?
      (d) How does air resistance (drag) effect the range of a projectile?  How does it effect the maximum height
            achievable?
      (e) How does the mass of a projectile effect the range if all other factors are constant?

Internet Resources:

 http://home.a-city.de/walter.fendt/phe/projectile.htm
 http://www.msu.edu/user/brechtjo/physics/cannon/cannon.html

3.   (a)  Why does the banana miss the monkey when launched in the absence of gravity?
      (b) In the presence of gravity, when should the monkey let go of the limb if he wants to catch the banana?
           Explain.
      (c) Does gravity effect whether or not the monkey will catch the banana?  Explain.

Internet Resources:

 http://www.glenbrook.k12.il.us/gbssci/phys/mmedia/vectors/mzi.html
 http://www.scienceprof.com/members/swf/monkey1.swf
 
 

4.   (a) What are the equations that must be used for finding the range, height and time in air of a projectile
             launched from any angle?
      (b) How are these equations similar to those of objects moving with linear motion in one direction?
      (c) What additional factor must be considered in the equations for parabolic flight that need not be considered
            in linear flight?

Internet Resources:

 http://www.glenbrook.k12.il.us/gbssci/phys/Class/vectors/u3l2d.html
 
 

It should now be apparent that in order to calculate the landing point of a projectile launched at an angle to the horizontal, the initial velocity of the projectile must be known.  Perform the following activity as discussed below and apply knowledge gained in order to calculate the initial velocity of your projectile launcher so that you may use that information in pre calculating the landing point of a golf ball.  The premise that is understood here is that all objects fall to earth with the same acceleration regardless of their mass (assuming that they are nearly identical in aerodynamic composition).

1.  Clamp a metal ball launcher to the table top, making sure that it is parallel with the floor.
2.  Fire the metal ball with the lever pulled back to exert maximum force.  Watch where it lands.
3.  Tape a piece of white paper or two in the general landing area.
4.  Wet the ball and launch the ball five (5) times, marking the spot in which it lands each time.
5.  With these data points and the measured height of the projectile from the floor when it is launched, calculate five
     (5) velocities and find their average.  This will now be accepted as the initial velocity of the launcher.
6.  Now set the launcher to an arbitrary angle with the table.  Carefully measure the angle and record it.
7.  Calculate the point at which the ball will hit the floor, remembering to take into account the fact that it rises
     above the level of the table before it falls back to the level of the table on its downward path.
8.  Place a piece of paper at this point and, when ready, launch the metal ball.
9.  Measure the distance between your calculated value and the actual landing point and record as your absolute error.  Measure the actual distance traveled and record this as "A".  Calculate your relative error.
10. It is time now for you and your group members to brainstorm how you might build a launcher that will project a golf ball into the air at some angle and how you would go about pre calculating its landing point.

Purpose:

The purpose of this project is the construct a machine that will launch a projectile (golf ball), with a pre-determined velocity, at a pre-determined angle and have it land at a pre calculated landing point.  No catapults are allowed.

Scoring:

 The scoring of this project will be based upon the following criteria:

1.   Accurate Specifications:
      · The machine launches the projectile both horizontally and at an angle.
      · The force the machine gives to the projectile is reproducible (produces
        the same force over many trials).
      · The machine launches the projectile with a force large enough to
        accelerate it a minimum distance of 5 meters from the end of the launcher.
      · The angle at which it launches is measurable and easily reproducible.

2.    Blueprints must be submitted at least one week prior to the initial launch.  All blueprints must be on
       graph paper, in ink and to scale.

3.    Your goal is to have your projectile land at the pre calculated location. Part of your grade will be
        based on  how close you come to that location.

4.    On launch day, you are to submit to your teacher a completed set of data and
       calculations, word- processed and in correct form.  Data and calculations must include
       both those completed for determining the initial velocity of your machine as well as those
       completed for determining the range of your projectile.

5.     Each student will complete a group assessment that will indicate to your teacher how well
        members of each group participated in the entire process of planning, constructing and
        processing the information required.

6.     Each group will be allowed one re-engineering of their machine in order to achieve better, more
        accurate results. If re-engineering becomes necessary, blueprints of the re-engineered machine
        must be submitted on the second launch date along with a new set of data and calculations,
        word processed and in correct form.
 
 

 Scoring Guide for Accurate Specifications:
0.   No project submitted
1. Project submitted
2. Approaches expectations
3. Meets expectations
4. Exceeds expectations

  Accurate Specifications:
· Machine launches the projectile horizontally and at an angle.
· The force is reproducible (produces the same force over many trials).
· Machine launches the projectile with a force large enough to accelerate the ball a
  minimum distance of 5 meters from the end of the launcher.
· The angle at which it launches is measurable and easily reproducible.

  Scoring Guide for Data and Calculations:
0.  No data or calculations submitted.
1.  Some data and calculations submitted
2. All data and calculations submitted.
3. All data and calculations submitted in correct form and word-processed.
4. Data and calculations exceed expectations.

  Scoring Guide for Relative Error:
0. No machine submitted
1. 51-100% error
2. 31-50% error
3. 11-30% error
4. 0-10% error

  Scoring Guide for Blueprints:
0. No blueprints submitted
1. Blueprints submitted
2. Blueprints address criteria
3. Blueprints nearly meet criteria
4. Blueprints submitted to scale, on graph paper and in ink

  Scoring Guide for Group Assessment:
0. No participation
1. Some participation
2. Approaches expectations with participation
3. Meets expectations of participation
4.  Exceeds expectations of participation