Projectile Motion

Jan Dudzik                 Riverside-Brookfield High School
10025 Medill               First and Forest Ave. 
Melrose Park IL 60164      Riverside IL 60546
708-455-0599               708-455-7500 
                                       
Objective:

As a result of this experience students will:

      1. be able to recognize that projectile motion is the resultant of 
         two independent velocities, horizontal and vertical. 
      2. determine which angle of launch for a projectile will yield the 
         greatest range. 
      3. realize that the greater the angle of launch, the greater the vertical 
         velocity component.

Materials:

For each group:  2 pieces of foam board 90 cm. x 50 cm., Sheet of paper 70 cm.x 
70 cm., Tape, Meter Stick, 4 different colored markers, Angle launcher, Spring.

Strategy:

     Roll a ball across the table.  Ask the students to define this motion.  Throw a 
ball straight up into the air.  Ask the students to define this motion.  Using 
the responses, establish that both objects follow a straight line path, but that 
one path is in a vertical direction and the other is in the horizontal 
direction. 
     Next, have a student throw a ball across the room into a garbage can held 
by another waist high.  Instruct the students to watch carefully and repeat this 
2 times. Ask students to write down how they would define this motion, under the 
heading Day 1 on their record sheet.  Collect these Pre-Activity student 
responses and read some out loud. 
     Set the stage for the activity by pointing out that they will be 
investigating how the parabolic path of a projectile is formed.  Hand out 
instructions and let the groups work together for about 20 min. 

....DAY 1....                  INSTRUCTIONS PART 1
1. Tape a large blank 50 cm. x 50 cm. paper to the table.  
2. Draw a 40 cm. line straight up the paper about 4 cm. away from the vertical 
edge of the paper.  
3. Draw another 40 cm. line across the paper about 4 cm. away from the 
horizontal edge of the paper. 
4. Extend the lines so that they meet at one point in the left hand corner. 
5. Next, measure about 4 cm. starting from the corner where the lines meet, up 
along the vertical line and mark it with a dot.  This will be the starting point
for the vertical foamboard. 
6. Repeat step 5 for the horizontal axis. 
7. Line up one piece of foamboard so that the bottom edge of the foamboard lies 
just above the horizontal line on your paper.  Guide this board along the 
horizontal line until it's vertical edge is on the horizontal starting dot.  BE 
SURE the entire bottom is just above the horizontal line and the vertical edge 
begins on the horizontal starting dot. 
8. Line up the other piece of foamboard so that the vertical edge lies right
next to the vertical line. Guide this board along the vertical edge until the 
edge is on the vertical starting dot. 
9. Place the marker down at the corner point where the two foamboards meet. 
10. Move both foamboards at about the same SLOW speed simultaneously along their 
respective lines while the marker moves to stay in contact with the moving 
corner where the foamboards meet, so as to trace a line on the paper of the 
movement of the corner.  
11. Move until both foamboards have reached the end of their lines. 
12. Place boards back to their starting points and this time have the vertical 
foamboard move a little faster than the horizontal foamboard and again trace the 
path of the moving corner where the boards meet. (use a different color marker) 
13. Repeat again, but this time have the vertical foamboard move more slowly 
than the horizontal board. 
14. Write your names on your sheet and return to class. 
                               After 20 minutes:  
Have the students tape their data sheets on the board.  Note the similarities. 
Next, use one of the graphs to establish that the path is the result of two 
independent velocities by drawing the components.  Then, hand out instructions 
for Activity 2 and instruct the students to notice what happens when you change 
the vertical velocity but keep horizontal velocity constant. 

....DAY 2....                  INSTRUCTIONS PART 2
1. Get a new sheet of paper and repeat steps #1-7 from Part 1.  Redraw the axis 
with starting dots. 
2. Now, mark a line 30 cm. away from the starting dot on the vertical line. 
3. Next, line up foamboards as you did in part one steps 7, 8, and 9.  For this 
trial have the vertical and horizontal boards begin at the SAME SPEED, but as 
the vertical board reaches the 30 cm. mark it should stop and begin to move back 
to it's original starting dot.  During this trial the however, the horizontal 
board should move the same speed its entire trip. 
4. Move the boards back to their starting position and, for this trial, have the 
vertical board go FASTER than the horizontal board to begin with but have the 
vertical board slow down, stop at the 30 cm. mark, and then go back down to it's 
starting mark. (Horizontal should go slow the entire trip.) 
5. Repeat, this time have the vertical board go SLOW, come to a complete stop 
at the 30. cm. mark, and then go back down to it's starting point.  Horizontal 
should go slow the entire trip. 
6.Place the names of the students on the sheets and tape them to the blackboard. 
                               After 20 minutes:
Point out similarities between the group graphs.  Call attention to the fact 
that the greatest angle formed by a resultant path was due to a large vertical 
velocity combined with a small horizontal velocity.  Ask the students to guess 
what angle to shoot a projectile so that it would go the farthest.  Record their 
predictions.  Review at this time the sine and cosine trig functions.  Remind 
the students that this case is geometrically similar and review free fall 
equations.  Hand out a worksheet and have the students draw the components of 
given vectors.  Set the stage for the last activity by pointing out to students 
that to investigate which angle yields the greatest range they must keep the 
initial velocity of the projectile the same in each case. 

.....DAY 3....               INSTRUCTIONS PART 3
1. Hold a meter stick against the wall. Mark a 1 meter mark with tape and then 
measure up 2 more m. and mark with tape.  
2. Stretch a spring on a meter stick, hold it parallel to the wall and then 
shoot the spring straight up. Do this several times until you can repeat a shot 
to go exactly 2 m. several times. Write down how far you stretched the spring. 
Get an assigned angle for your launch from your teacher.  (TEACHER: assign 15o, 
30o, 45o) 
3. Calculate the speed at which the spring is fired, use the equation 
   v2 = 2 ad .
4. Determine the vertical and horizontal components of the original velocity by 
using vv= v sin(angle) and vh = v cos(angle)
5. Use the vertical velocity to find the flight time, t = 2vv/a.
6. Use the flight time and the horizontal velocity to calculate the range  
d=vhtf
7. Measure off this distance and shoot the spring using the same stretch.

Performance Assessment: 

BEFORE the instruction begins have the students answer: 
1. If a baseball player throws the ball as hard as he can, and wants it to go 
as far as possible, should he throw at an angle to the ground >45,<45 or = 45 ? 
AFTER Instruction:
2. The human cannonball is shot at a 30 degree angle with a velocity of 
10 m./sec.  Determine where they should place the net to catch him.
3. The following is a strobe picture of the human cannonball's ride.  At the 
spots marked, draw the vertical and horizontal components of velocity.
4. Assuming that the initial velocities of the missiles are the same, draw the 
paths of missiles shot at the following angles: 15o, 30o, 45o, 60o.