Return to Physics IndexProjectile Motion

Jan Dudzik Riverside-Brookfield High School

First and Forest Ave.

Riverside IL 60546

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 15^{o},

30^{o}, 45^{o})

3. Calculate the speed at which the spring is fired, use the equation

v^{2}= 2 ad .

4. Determine the vertical and horizontal components of the original velocity by

using v_{v}= v sin(angle) and v_{h}= v cos(angle)

5. Use the vertical velocity to find the flight time, t = 2v_{v}/a.

6. Use the flight time and the horizontal velocity to calculate the range

d=v_{h}t_{f}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: 15^{o}, 30^{o}, 45^{o}, 60^{o}.