```Projectile MotionJan 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 11. 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 pointfor 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 rightnext 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 21. 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 31. 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.   ```
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