This work was supported by the National Science Foundation under a RET Site Grant 0227479.

The goal of this project was to create a device that would model the physical laws in projectile motion. Using electronic and mechanical devices (mechatronics), a projectile launcher was built. This launcher will be used in a high school physics classroom to demonstrate the laws of projectile motion. When an appropriate angle (20 to 65 degrees) is entered in the software program the basic stamp raises the platform, computes the correct distance for the "catcher" and finally launches the ball towards the target. It was found that the device was consistently accurate for angles from 20 to 30 degrees. When other factors were included in the formula, the accuracy was extended from 20 to 65 degrees. It was discovered that errors in the creation of the device and the limits of the basic stamp were likely to effect the outcome of this experiment.



When objects are thrown or fired from the Earth's surface their trajectory can easily be determined
by using the laws of physics. These laws govern the distance that a projectile will travel across the
surface of the Earth. By changing the angle at which a projectile will launch, one can determine the
maximum distance that it will travel for a given velocity. One military application of this can be
found in the field of artillery. When the initial velocity can be determined, it is relatively easy to
determine the correct distance that a shell will travel. These calculations are typically very accurate
however error does exist. One error that must be taken into account is air resistance which acts as a
retarding force on the projectile. Another possible error is the Coriolis Effect that is caused due to
Earth's rotation. This effect is only a serious consideration when a projectile is in the air for are
extended period of time.


This project meets the New York State Education Department Physics Standards in the following way;

Science Standards-Commencement Level
Key Idea 4:
4.1 Energy exists in many forms, and when these forms change energy is conserved.
· describe and explain the exchange among potential energy, kinetic energy, and internal energy for simple mechanical systems, such as a pendulum, a roller coaster, a spring, a freely falling object.
· observe and explain energy conversions in real-world situations

Key Idea 5:
5.1 Explain and predict different patterns of motion of objects (e.g., linear and uniform
circular motion, velocity and acceleration, momentum and inertia).
· sketch the theoretical path of a projectile

5.1f The path of a projectile is the result of the simultaneous effect of the horizontal and
vertical components of its motion; these components act independently.

5.1g A projectile's time of flight is dependent upon the vertical component of its motion.

5.1h The horizontal displacement of a projectile is dependent upon the horizontal component
of its motion and its time of flight.


Illustration 1. Projectile Motion

Projectile Motion describes the motion of an object, in at least two dimensions, and experiences that force of gravity in the vertical direction. The motion of a projectile can be analyzed separately as two independent motions, horizontal and vertical. A projectile launched at some angle theta and initial velocity Vo will have a horizontal velocity component of Vocos ? and a vertical velocity component of Vosin theta.

A projectile's horizontal velocity is constant because it experiences no net force in the horizontal direction. A projectile's vertical velocity is not constant as it experiences a net force downward, equal to the weight of the object. This net force results in an acceleration according to Newton's 2nd law and is equal to 9.8 m/s2 downward. For the case when the launch height is equal to the landing height, the time of flight can be found by first finding the time the projectile takes to reach its maximum height. The vertical velocity of the projectile is zero at this point and this fact can be used with the equation that describes the velocity of an accelerated object to find the time.
The time of flight will then be two times the time found above. The time of flight can now be used with the equation that describes the horizontal displacement to find the range of the projectile.




The mechanical device used to launch the golf ball is a converted Wilson Putting Pal(shown below).


In order to "catch" the golf ball a track was built. The catcher was constructed from a piece of lucite with ball bearings drilled into it. These ball bearings allowed the catcher to move freely along two supporting metal rods. The catcher was driven by a servo motor (shown below), with a gear attached, which was used to move the catcher to a specific point along the track.



Procedure: Verification of Projectile Motion Formula

1. Students will relate the angle of release to the maximum horizontal distance that the projectile travels.
2. Students will identify the angle (450) of maximum horizontal displacement.

1. Connect BS2 to the breadboard by using the DB-15 adapter and to a computer using a DB-9 serial cable.
2. Download the CatchMeIfYouCan.bs2 file to the BS2
3. At the prompt, the student will enter the desired angle (20-65 degrees) in the window.
4. The BS2 will elevate the platform to the desired angle, student will be instructed to place golf ball in launcher.
5. The BS2 will determine the proper distance to move the "catcher" on the track. The servo motor will move "catcher" to calculated position.
6. Ball will be launched and will land on catcher.

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It was determined that the projectile launcher was accurate for angles from 20 to 30 degrees. When tested at these angles the ball constantly hit the catcher. However at angles above 30 degrees, the ball was consistently short of the catcher, which was correctly placed based at the calculated distance.
distance. This effect was more pronounced as the angle increased. We believed that this effect was due to the position of the golf ball in the launcher. At high angles, the motor was unable to produce the velocity (3 meters/second), required to propel the golf ball. We changed the formula so
that the range of the catcher was reduced by the angle of the launcher minus twenty five. After further testing it was determined that the apparatus was now accurate between the angles of 20 and 65 degrees.


A) Floating Point Calculations
One unavoidable error in this experiment is due to the limitations of the BS2. The BS2 is unable to make floating point calculations, such as including the decimal point placement in a calculated number. This means that many calculated numbers will not be rounded off correctly. It has been determined in this experiment that this could lead to an error in distance of up to three centimeters. In order to round numbers off to an acceptable level, another limitation of the BS2 comes into play. The largest variable that can be stored in the BS2 is a "word" which has a numerical range of 0-65,535. This indicates that the highest level of precision in this experiment cannot exceed the thousandth placement.

B) Initial Velocity of the Golf Ball
In this experiment the initial velocity of the golf ball is assumed to be a constant. In fact the initial velocity of the ball is highly influenced by the voltage applied to the solenoid in the launcher. Since the voltage applied to the solenoid can vary in small amounts, the initial velocity of the golf ball will have a range of values. Since the velocity of the ball is not being determined in this experiment, it cannot be used in the formula. In order to account for this range of velocities, a larger "catcher" has been used. This will allow for variations in initial velocity.

C) Mechanical Hinge
The hinge that was constructed to open the platform allows for some "play" in the angle of the platform (see image below). When the platform is raised to the desired angle, the hinge is unable to hold that angle exactly due to the mass of the platform, golf ball and launcher. This results in a small drop in the position of the platform before the golf ball is released.

Full project in .pdf format