ED 5661 Mathematics & Navigation Teacher Institute Kevin Murphy 12 August 2011 Grade 11/12 Average Velocity and Speed on a Boat Trip – Teacher’s Resource Page Lesson Overview: In this lab activity, students will use vectors to determine the average velocity and average speed during a boat trip. Sources: 
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Brogan, Bill. Boat Navigation for the Rest of Us, 2nd Ed New York: International Press, 2001. Print. Roblee, Stephen . ED 5661 Mathematics & Navigation Teacher Institute. Michigan Technological University. Houghton, MI, June 2011. Activity 5. Materials: Navigational Map (provided by instructor), Rolling Ruler, Calculator Vocabulary: (These terms will have been covered in previous classes, but are presented here for review). Before beginning this activity, please review these terms: 
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Vector Scalar Displacement Average Velocity Average Speed Focus [Pre‐Activity] Questions: 1) What is the primary difference between the way a boat travels between two points and the way a car travels (on streets) between two points? 2) A boat travels at 8 m/s for 10 min and then at 12 m/s for 20 minutes. What is the boat’s average speed? [Hint: The answer is NOT 10 m/s] Learning Objectives: 
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Students will be able to calculate the velocity of each path segment along the course (determined by the instructor). Students will be able to calculate the average velocity of the entire trip. Students will be able to calculate the average speed of the entire trip. Benchmarks: 
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Illinois Math Performance Descriptor: 9D, Stage, Stage J, Solve Problems Using Vectors Common Core State Standards for Mathematics: Vector and Matrix Operations, 4. Add and Subtract Vectors. Activity Description: Students will use a map (attached) and plot out a course from Point A to Point B. The choice of paths is somewhat confined, so answers will fall within a reasonable range. The assumption here is that each leg requires the same amount of time, so students can determine the velocity during each leg as well as the average velocity for the entire trip. Assessment: The following questions conclude the activity and serve as an assessment of students understanding of the concepts. Since paths will vary, no two students will have exactly the same answers. Ranges for the answers are included. 1. During which leg of the trip did your boat have the greatest velocity? 2. What was the average speed of your boat during the trip? [Show your work below]. Average Velocity and Speed on a Boat Trip Lesson Overview: In this lab activity, you will use vectors to determine the average velocity and average speed during a boat trip. Materials: Navigational Map (provided by instructor), Rolling Ruler, Calculator Vocabulary: (These terms will have been covered in previous classes, but are presented here for review). Before beginning this activity, please review these terms: 
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Vector Scalar Displacement Average Velocity Average Speed Pre‐Activity Questions: 3) What is the primary difference between the way a boat travels between two points and the way a car travels (on streets) between two points? 4) A boat travels at 8 m/s for 10 min and then at 12 m/s for 20 minutes. What is the boat’s average speed? [Hint: The answer is NOT 10 m/s] Learning Objectives: 
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You should be able to calculate the velocity of each path segment along the course (determined by the instructor) given the time and measuring the length of the segment. o For our purposes, consider 1.0 mm = 50 meters You should be able to calculate the average velocity of the entire trip. You should be able to calculate the average speed of the entire trip. Activity Description: 1. Plot a course (on the attached map)from Point ‘A’ to Point ‘B.’ a. The course should begin between the two buoys (near Point ‘A’) and end at the buoy labeled G”3”. b. Your course needs at least 3 legs and must stay in water in which a boat can travel. 2. Once you have drawn the course, use a rolling ruler to measure both the length and direction of the distance segment. a. Note: Use the “True North” values for direction b. Record these in the table on the following page. c. Velocity (m/s) Segment # Time (mm:ss) Distance (m) Direction (degrees) 1 08:30 2 08:30 3 08:30 4 08:30 3. For the purposes of this lab, we will assume that the boat covered each leg of its journey in the same amount of time. This obviously means that its speed changed during the trip. a. Determine velocity of the boat for each leg of the trip. b. Record these values in the table above. Record these values in the table above. 4. Answer the questions below in the space provided. Assessment Questions: 3. During which leg of the trip did your boat have the greatest velocity? 4. What was the average speed of your boat during the trip? [Show your work below]. 5. What was the average velocity of your boat during the trip? [Show your work below]. A B