# The Physics of Rocket Trajectories

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1 The Physics of Rocket Trajectories Objectives Students will recognize and use the interconnectedness of various physics ideas and formulas. Students will construct a model rocket and use physics to assess its initial velocity. Students will use scientific estimation techniques to gain measurements of rocket trajectories. Students will critically examine their rocket to assess drag. Grade Level Subject Area(s) Physics Algebra I Geometry Simple trigonometry Timeline Three 90-minute blocks Background This lesson is part of an introductory physics course. Students must have studied linear motion, projectiles, and Newton s 3 laws. This lesson fits into a study on potential energy, kinetic energy, and the conservation of energy. Materials Estes Alpha model rocket. (Approximately \$6 each) These rockets can be bought in bulk packs with a teacher s discount through 2 engines for each student. Model rocket launch pad and launch pad controller Calculators Extra sheets of balsa wood Class set of model paints Elmer s glue Styrofoam cups Craft knives Materials for altimeter (straws, protractor copied on paper, string, small weight such as washer or small rock, hot glue gun) Lesson Day One 1. Debrief students on safety issues dealing with model rocketry. (You might want to give the students a list of safety guidelines prior to this day and present a quiz to them this day, which they have to complete with a 90% or better before proceeding.) 2. Present task that students must complete:

2 Students must build fins for an Alpha rocket so to reach maximum initial velocity and therefore maximum height in their class. (You should tell the students that each rocket needs at least 3 fins to fly.) Conditions: a. Students must be prepared to justify their choices for fin structure later in the activity. b. The initial velocity must be calculated two different ways from the measured height. 3. Construction of Model Rockets: 4. Before the students receive the rockets remove the Estes provided fins and replace with a sheet of balsa wood 5 x Have students open the packaging and collect the launch lugs in the interest of them not being lost. 6. Give each student a Styrofoam cup and have them cut a hole in the bottom of the cup the size of the rocket diameter to be used as a stand. See picture below a. Give each student a craft knife and individual Elmer s glue. b. Go through the instructions with the students and check for correct construction after each step. c. Try to prevent students from working ahead. d. Extra time will be required during the fin cutting so students can figure out what they actually want to do. e. You can save showing the students how to properly stuff the parachute into the rocket until day Homework f. Students will paint and use decals to finish off their rocket. g. Instruct the students to use model paint verses spray paint. h. It is a good idea to have a class set of model paints so students can come in after school to paint their rockets if they cannot afford to purchase paints at home. i. On a block schedule the students will have at least 4 evenings to complete this. Day Two ***Remind students that the painted model rockets will be due the next day. 1. Discuss the physics of the task the students will be completing. a. We must first calculate h for the rocket. This will be done using an altimeter; directions for constructing the altimeter are below. 1) Copy a 3-4 protractor on a piece of paper. Hot glue a straw lengthwise on the bottom of the protractor. At the center point attach a string with a weight at the end of it.

3 2) To find the angle when the rocket is at its maximum height, find the rocket looking through the straw and have a friend read off the angle, the angle you need, θ, is 90 o minus this angle. To find the height of the rocket with the angle you must use some basic trigonometry. You should probe the students on how to find h if you know the angle and the distance, d, from you to the launch pad. h cos θ = d h θ d 2. Have the students bring in the altimeter with the rocket to class with them tomorrow. a. Once h is found, we can calculate v 0 for the rocket using projectile motion equations and the conservation of energy. 1) Refresh the students of projectile motion equations. 2) h = ½ gt 2 + v o t 3) Ask the students what you need to know to find v o besides h. (Answer: g,t ) What is g? What will we need to measure t? 4) Give the students the Tutorial on Conservation of Energy (attached). This will review with the students that initial KE = ½ mv 2 o and that at the top of the arch PE = mgh. Because PE = 0 at launch and KE = 0 at the top of the arch than all KE must turn into all PE so KE = PE and ½ mv 2 o = mgh and finally 5) ½ v 2 o = gh since the mass is the same. Day Three: 1. Launch rockets. Students should have brought their painted rockets in. Each student will get 2 launches so you will need 2 engines per student. 2. Have students find h when their rocket is launched using their altimeter and trigonometry. 3. Have students finish the worksheet (attached) before they leave class that day. Extensions You can use the specs on the Alpha rocket provided by Estes rockets to study thrust or specifics on rocket trajectories. This would probably be more suitable for an AP physics course. Evaluation/Assessment Embedded: Monitor students comprehension of construction techniques during model rocket building. Monitor individual students or groups of students working on conservation of energy tutorial. Formal assessment: Worksheet that individual students work on upon completion of rocket launches. Resources This lesson is adapted from materials distributed from Space Discovery Graduate Course, Space Law, Space History, Rocketry, and Biological Research.

4 Estes Educator Website: Addendum Name Tutorial on Conservation of Energy Fill in the blanks in the following diagram: 1. What happens to the 10 J of KE at the top of the arc? 2. So initial KE = 3. So if KE = ½ mv o 2 and PE = mgh then ½ mv o 2 =. 4. Are the m s the same number? 5. So ½ v o 2 =. 6. What is g? So what else do we need to measure to find v o using the conservation of energy?

5 Name Analyzing your rocket 1. What does your fin structure look like? (Draw a picture of your rocket.) 2. Why did you choose that fin structure? Go through each feature of your fins and justify. 3. Rocket launch information: Trial 1 Trial 2 Maximum height (m) Choose the largest height and solve for Vo using projectile motion equations and the conservation of energy. Show all calculations. Projectile motion eqns: Conservation of energy: 4. Did you get the same answer for both? Why does it have to be the same? (Answer with a few sentences.)

6 5. Compare your Vo with others you know, how does yours compare? 6. Look carefully at your fin structure If your rocket was relatively slower, why do you think so? If your rocket was relatively faster, why do you think so? 7. How do you think painting/decals affected the rocket performance?

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