```PROJECTILE MOTIONCunningham, Mary M.               Resurrection High School                                  1-312-775-6616                           OBJECTIVES

To measure muzzle velocity of a projectile device.
To predict maximum range of a projectile device at various angles.
To measure range of device at various angles.

APPARATUS NEEDED

Calculator, Tape measure, stopwatch, projectile device, projectiles. (This
demonstration used a "Lobster," a device used in training tennis players.)

RECOMMENDED STRATEGY

1.   Throw a ball or frisbee out to groups of students.  Ask students to toss the
ball back and forth.  Have students jot down their observations and and a description
of the motion of the ball.

2.   Introductory discussion:  What name could we give to this category of objects?
(PROJECTILES) Can you think of some other projectiles?  What are some of the
characteristics of projectiles in motion?  (List all suggestions on board or
overhead.  If necessary elicit the following terms: velocity, acceleration, time,
horizontal motion, and vertical motion.

3.   Explanation:  In order to analyze projectile motion with all the listed
characteristics, we would need a NASA computer.  We are going to ignore all factors
except velocity, acceleration and time.  If necessary review horizontal velocity and
vertical velocity.

4.   Presentation of activity:
a.   Work in lab groups.

b.   Explain use of the projectile device. The muzzle velocity can be determined
by aiming the muzzle straight up.  Record the time required for the
projectile to leave the muzzle and return to the ground.  Do 5-10 trials,
find the average round trip time.

c.   Choose 2-3 angles. Predict the range using vector analysis and trig
calculations.  (See Math Notes) Use the projectile device, measure the
range of the projectiles.  Compare projected range with actual range. What
are the sources of error? (Consider using complementary angles)

5.   Post activity discussion: Explain why there were differences between predicted
and experimental value of range. What were the variables? How could variables be
controlled?  What conditions would optimize experimental values?  How could
experiment be improved?  What other ways could projectile motion be tested?

NOTES

1. Non-Math oriented classes:  This activity can be modified for use with students
who are not in high school physics.  Students could be asked to predict which angle
will make the ball go further.  They can begin with actually testing the device and
could graph the angle vs. distance shot.

2.   Math Notes

Muzzle Velocity  V(muz) = A * T
Where A is the acceleration of gravity and                         T is half the round trip time for a ball                              shot directly upward.Range Calculations The muzzle velocity does not change as the angle is changed.  It                    can be resolved into a vertical and horizontal component.                     Consider the angle with the horizontal to be Theta then                          V(ver) = V (muz) * sin Theta and                         V(hor) = V (muz) * cos Theta
The time of flight can be calculated using the formula, V(ver) = A
* Tup and solving for Tup.                    Time of flight is 2 * Tup.                   Since the V(hor) is not accelerated,                    Range = V(hor) * time of flight
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