Enhanced Learning Strategies for Vector-Related Concepts
Explore a structured recitation session focusing on average quantities in vectors, including warm-up activities, conceptual discussions, and problem-solving. Engage in infographics, qualitative questions, and analytical problem-solving to deepen understanding of vector concepts.
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Presentation Transcript
PH201 Recitation 2 Average Quantities (Vectors)
General Outline 5 minutes: Warm up with infographics or similar style of questions 10 minutes: Conceptual and qualitative discussion based questions, some multiple select questions 20 minutes: Large scaffolded question, demonstrate sensemaking throughout, go through complete solution 10 minutes: Large question, similar to challenge homework, get through setup/problem orientation 5 minutes: Wrap up, metacognitive discussion about the learning goals of the day
Warm-Up 1: 1 minute Label each of the following quantities Write down the equation in words To find the infographics on BoxSand go to Tips & Tricks => Mathematical Representation
Warm-Up 2: 1 minute Label each of the following quantities Write down the equation in words To find the infographics on BoxSand go to Tips & Tricks => Mathematical Representation
Warm-Up 3: 1 minute Label each of the following quantities Write down the equation in words To find the infographics on BoxSand go to Tips & Tricks => Mathematical Representation
Warm-Up 4: 1 minute Label each of the following quantities Write down the equation in words To find the infographics on BoxSand go to Tips & Tricks => Mathematical Representation
Discussion Question 1: 3 minutes 1) A person in a car is driving down a straight road. The car has constant acceleration in the direction of the car s motion. The speed of the car is A) increasing with time B) decreasing with time C) constant 2) Now the car has constant acceleration opposite the direction of the car s motion. The speed of the car is A) increasing with time B) decreasing with time C) constant
Discussion Question 2: 3 minutes Shown here are the velocity and acceleration vectors for an object in several different types of motion. In which of the cases is the object slowing down and turning to its right? Teachers guide: talk about all 5, finish discussion with d) and what happens after a few moments and what the motion does
Discussion Question 3: 3 minutes In which of the following situations does the car necessarily have a westward acceleration? A) The car travels westward and is slowing down B) The car travels westward and is speeding up C) The car starts from rest and moves toward the east D) The car starts from rest and moves toward the west E) The car travels eastward and is slowing down F) The car travels eastward and is speeding up
General Outline of Scaffolding: 20 min Problem Orientation: 8 min 1. Read the problem entirely, visualize and make sense of what s going on: 2 min 2. Discuss with your group: 1 min 3. Individually draw your physical representation: 2 min 4. Compare with your group and come to consensus: 1 min 5. List knowns and unknowns: 1 min 6. What s being asked and what physics is needed to solve the problem: 1 min Solve each part of the problem: 12 min 1. Part a) and use sensemaking tools (sign/direction and dimensionality): 2 min 2. Go over part a) together: 2 min 3. Part b) and use sensemaking tools (sign/direction and order of magnitude): 2 min 4. Go over part b) together: 2 min 5. Part c) and use sensemaking tools (sign/direction and order of magnitude): 2 min 6. Go over part c) together: 2 min
Problem of the Day Step 1: Read and Visualize: 2 min After being kidnapped and placed in a trunk of a car, you discover you are able to pry open the trunk. Luckily your smart phone has a gps that receives signal when you open the trunk. The gps tells you that you re moving 25.0 mph in a direction of 66 north of east at a location 1.33 miles west of the police station. You then close the trunk so as not to be spotted. 5 minutes later you take another reading that says you are now 2.1 miles north of the police station and are moving east at a speed of 5 mph. A) What was your average velocity during this trip? B) What was your average acceleration during this trip? C) What is the distance and direction you would need to travel to return to the location of your first gps reading if you jumped out of the car now? (assume your phone breaks during your collision with the ground)
Problem of the Day Step 2: Discuss with Group: 1 min After being kidnapped and placed in a trunk of a car, you discover you are able to pry open the trunk. Luckily your smart phone has a gps that receives signal when you open the trunk. The gps tells you that you re moving 25.0 mph in a direction of 66 north of east at a location 1.33 miles west of the police station. You then close the trunk so as not to be spotted. 5 minutes later you take another reading that says you are now 2.1 miles north of the police station and are moving east at a speed of 5 mph. A) What was your average velocity during this trip? B) What was your average acceleration during this trip? C) What is the distance and direction you would need to travel to return to the location of your first gps reading if you jumped out of the car now? (assume your phone breaks during your collision with the ground)
Problem of the Day Step 3: Draw a Picture: 2 min After being kidnapped and placed in a trunk of a car, you discover you are able to pry open the trunk. Luckily your smart phone has a gps that receives signal when you open the trunk. The gps tells you that you re moving 25.0 mph in a direction of 66 north of east at a location 1.33 miles west of the police station. You then close the trunk so as not to be spotted. 5 minutes later you take another reading that says you are now 2.1 miles north of the police station and are moving east at a speed of 5 mph. A) What was your average velocity during this trip? B) What was your average acceleration during this trip? C) What is the distance and direction you would need to travel to return to the location of your first gps reading if you jumped out of the car now? (assume your phone breaks during your collision with the ground)
Problem of the Day Step 4: Discuss with Group: 1 min After being kidnapped and placed in a trunk of a car, you discover you are able to pry open the trunk. Luckily your smart phone has a gps that receives signal when you open the trunk. The gps tells you that you re moving 25.0 mph in a direction of 66 north of east at a location 1.33 miles west of the police station. You then close the trunk so as not to be spotted. 5 minutes later you take another reading that says you are now 2.1 miles north of the police station and are moving east at a speed of 5 mph. A) What was your average velocity during this trip? B) What was your average acceleration during this trip? C) What is the distance and direction you would need to travel to return to the location of your first gps reading if you jumped out of the car now? (assume your phone breaks during your collision with the ground)
Problem of the Day Step 5: Knowns/Unknowns: 1 min After being kidnapped and placed in a trunk of a car, you discover you are able to pry open the trunk. Luckily your smart phone has a gps that receives signal when you open the trunk. The gps tells you that you re moving 25.0 mph in a direction of 66 north of east at a location 1.33 miles west of the police station. You then close the trunk so as not to be spotted. 5 minutes later you take another reading that says you are now 2.1 miles north of the police station and are moving east at a speed of 5 mph. A) What was your average velocity during this trip? B) What was your average acceleration during this trip? C) What is the distance and direction you would need to travel to return to the location of your first gps reading if you jumped out of the car now? (assume your phone breaks during your collision with the ground)
Problem of the Day Step 6: Whats being asked: 1 min After being kidnapped and placed in a trunk of a car, you discover you are able to pry open the trunk. Luckily your smart phone has a gps that receives signal when you open the trunk. The gps tells you that you re moving 25.0 mph in a direction of 66 north of east at a location 1.33 miles west of the police station. You then close the trunk so as not to be spotted. 5 minutes later you take another reading that says you are now 2.1 miles north of the police station and are moving east at a speed of 5 mph. A) What was your average velocity during this trip? B) What was your average acceleration during this trip? C) What is the distance and direction you would need to travel to return to the location of your first gps reading if you jumped out of the car now? (assume your phone breaks during your collision with the ground)
Problem of the Day: Solve part a) and check sign/direction and dimensionality: 2 min After being kidnapped and placed in a trunk of a car, you discover you are able to pry open the trunk. Luckily your smart phone has a gps that receives signal when you open the trunk. The gps tells you that you re moving 25.0 mph in a direction of 66 north of east at a location 1.33 miles west of the police station. You then close the trunk so as not to be spotted. 5 minutes later you take another reading that says you are now 2.1 miles north of the police station and are moving east at a speed of 5 mph. A) What was your average velocity during this trip? B) What was your average acceleration during this trip? C) What is the distance and direction you would need to travel to return to the location of your first gps reading if you jumped out of the car now? (assume your phone breaks during your collision with the ground)
Problem of the Day: Solve part b) and check sign/direction and order of magnitude: 2 min After being kidnapped and placed in a trunk of a car, you discover you are able to pry open the trunk. Luckily your smart phone has a gps that receives signal when you open the trunk. The gps tells you that you re moving 25.0 mph in a direction of 66 north of east at a location 1.33 miles west of the police station. You then close the trunk so as not to be spotted. 5 minutes later you take another reading that says you are now 2.1 miles north of the police station and are moving east at a speed of 5 mph. A) What was your average velocity during this trip? B) What was your average acceleration during this trip? C) What is the distance and direction you would need to travel to return to the location of your first gps reading if you jumped out of the car now? (assume your phone breaks during your collision with the ground)
Problem of the Day: Solve part c) and check sign/direction and order of magnitude: 2 min After being kidnapped and placed in a trunk of a car, you discover you are able to pry open the trunk. Luckily your smart phone has a gps that receives signal when you open the trunk. The gps tells you that you re moving 25.0 mph in a direction of 66 north of east at a location 1.33 miles west of the police station. You then close the trunk so as not to be spotted. 5 minutes later you take another reading that says you are now 2.1 miles north of the police station and are moving east at a speed of 5 mph. A) What was your average velocity during this trip? B) What was your average acceleration during this trip? C) What is the distance and direction you would need to travel to return to the location of your first gps reading if you jumped out of the car now? (assume your phone breaks during your collision with the ground)
Challenge Homework Orientation: 10 min An aging coyote cannot run fast enough to catch a roadrunner. He purchases on eBay a set of jet- powered roller skates, which provide a constant horizontal acceleration of 15.0 m/s2. The coyote starts at rest 70.0 m from the edge of a cliff at the instant the roadrunner zips past in the direction of the cliff. A) Determine the minimum constant speed the roadrunner must have to reach the cliff before the coyote. At the edge of the cliff, the roadrunner escapes by making a sudden turn, while the coyote continues straight ahead. The coyote s skates remain horizontal and continue to operate while he is in flight. B) The cliff is 100 m above the flat floor of the desert. Determine how far from the base of the cliff the coyote lands. C) Determine the components of the coyote s impact velocity. Problem Orientation: 1. Read the problem entirely, visualize and make sense of what s going on: 2 min 2. Discuss with your group: 1 min 3. Individually draw your physical representation: 2 min 4. Compare with your group and come to consensus: 1 min 5. List knowns and unknowns: 1 min 6. What s being asked and what physics is needed to solve the problem: 1 min
Wrap-up: 5 min What did we learn today?
