Joy Paul Trajectory Motion

Main Objectives: Students will be able to: 1. Understand that a dropped object and an object that is projected will reach the ground at the same time due to the force of gravity. 2. Draw the trajectory path of a projectile (parabola). 3. Describe the changes in velocity of a projectile. 4. Calculate velocity of a projectile given V x and V y. 5. Predict how increasing the velocity and/or changing the launch angle of their projectile from a catapult will affect the range of the projectile.

Culminating activity: Students will form groups and using the above information build a catapult that launches a wet sponge. A contest will be held to see which group’s catapult launches the sponge the furthest distance.

Lesson plan: 1. Begin with thought question slides 2 and 3, leading class discussion toward the acceleration due to gravity (9.8 m/s²) being constant acting the same on all objects. Do demonstration with 2 balls, one projected off the table in the classroom, one dropped at the same time. Students should hear that both hit the floor at the same time. 2. To let students see the parabolic shape of a trajectory, bring students out into hallway and launch a soft ball or sponge from a catapult built by teacher. Recommended materials: 1 x 3 piece of wood for the launch arm cut to desired length, connected to a base piece of wood with a hinge. The base should have 2 vertical rectangular supports used for spring attachment. These can be strengthened with diagonal support struts if necessary. The other end of the springs should be attached to the launch arm. Pull back, and launch! Repeat as often as needed until all students see the shape of the trajectory. They will draw this shape on a piece of blank paper to be used for the next step. 3. Students will form small groups of 2 or 3 and label their parabolas with where they think the vertical speed of the sponge was increasing and/or decreasing. Teacher monitors group discussions. Each group presents their answers to the class. The decreasing speed as the sponge gets higher, the instantaneous velocity of zero at the top of the parabola, and the increasing velocity on the way down all due to gravity will be discussed using slides 4-6. Drawings will be corrected as needed. 4. In groups, students will discuss the answer to what gives the sponge, or any projectile, its distance. (Velocity in the “x” direction). The vector nature of velocity, the necessary formulas and how to use a calculator to find total velocity will be discussed using slides 7-10. Students will be given a worksheet (attached) to fill in with the correct formulas and practice calculations. 5. Students will be introduced to the range formula. R=V o²sin2θ g Each term’s definition will be discussed. A thought question will be provided as seen on slides 11-12. This will lead students to predict how changing the launch angle and/or increasing the velocity of the catapult they will build will help them gain a greater range and win the contest.

6. As a culminating activity, students will form groups and build a catapult that will launch a wet sponge. They will be provided with the same materials as the teacher demonstration model from step 2 above. However, to vary and control the launch angle, their launch arm will have a small eye hook in the back, where they will attach different lengths of string to control/limit the launch angle. The different lengths of string will halt the forward motion of the launch arm, thus providing an experimental variable. To vary the velocity of the launch arm, students will be provided with either different springs that each have a different tension, or, if appropriate, different numbers of rubber bands to increase or decrease the velocity of the launch arm. This provides students with another experimental variable to design a catapult that will give them the greatest range. Students will enter their catapults in a contest to see which group can launch a wet sponge the furthest on the sidewalk outside. The mark that the wet sponge leaves provides clear evidence of which sponge has the greatest range. Using chalk to label each wet mark with the group’s number is also helpful.

Challenge options: Provide student groups with a stopwatch to calculate trajectory time so that, using kinematic equations, they can calculate the velocity of their sponge. Using Newton’s second law, calculate the force needed to launch the sponge. Students may also see how varying the mass of the wet sponge affects the force needed for launch.

Vector/Velocity Practice Worksheet

1. Label the right angle and the hypotenuse of the triangle below:

2. Write the formula used to calculate the “x” or horizontal part of velocity: ______

3. Write the formula used to calculate the “y” or vertical part of velocity: ______

4. What formula do you use to find the total, combined velocity of a projectile? ______

5. Use your calculator to find the following:

A. sin 30 degrees______B. cos 45 degrees ______

C. 25 cos 40 degrees ______D. 30 sin 32 degrees _____

E. The initial velocity of a wet sponge was 10 m/sec. the sponge was launched at a 45 degree angle. What are the x and y parts of the initial velocity?

6. Use the range formula to calculate how far the sponge from “E” above should go.