Physics and the movement of boats – problem solving exercises: Physics and the movement of boats – problem solving exercises

Physics and the movement of boats – problem solving exercises

Physics

Lesson plan #2

ABOUT THE LESSON
Topic	Physics and the movement of boats – problem solving exercises
Duration	1 hour (45 min)
Assumed prior knowledge	Concepts studied with respect of the 2nd Principle of Mechanics: velocity, relative velocity, acceleration, inertial force, mechanical impulse (Lesson no. 1).
Goal(s) of the lesson	Knowing and understanding specific mechanical concepts. Development analysis and problem-solving skills, related to theoretical problems regarding the movement of boats.
The big idea behind the topic	Developing problem-solving skills. Establishing the units of measurement of the work given physical quantities. Correctly applying the formulas. Writing the mathematical sequences of calculating the formulas, specifying the significance of the occurring physical quantities. Discussing the solutions of the solved problems, comparing various results and methods used to obtain them.
Results of the lesson	Solving simple problems, related to the movement of boats, by applying laws of uniformly varied motion and the 2nd Principle of Mechanics formulas, based on mathematical calculation literacy.
Competencies	Specific competences: Fixing and consolidating the concepts studied in the second principle of mechanics: velocity, relative velocity, acceleration, inertial force, mechanical impulse. Formation and development of solving problems skills. Implementation of the main concepts: physical quantities, models, theories used in physics, in order to explain the laws according to which problem solving occurs. Derived competences: Establishing the units of measurement of the physical quantities to be worked with. Correct application of learned formulas. Writing the mathematical relations for calculating the formulas, specifying the meaning of the physical quantities involved. Solving simple problems by applying the specific formulas of the uniformly varied motion laws and the 2nd Principle of Mechanics, using mathematical literary calculation, and discussing the solution of the problem.
Methods	Teaching methods: Heuristic / learning consolidation conversation; Problematization; Analysis and synthesis; Systematization, algorithmization; Solving exercises and problems. Forms of activity: Frontal instruction – for knowledge updating; Individualized instruction – for presentations on the blackboard or whiteboard; Teamwork – for solving problems.
Relevance to the curriculum	Developing problem-solving skills. Establishing the units of measurement of the work given physical quantities. Correctly applying the specified or necessary formulas. Writing the mathematical sequences of calculating the formulas, specifying the significance of the physical quantities that occur. Solving simple problems by applying laws of uniformly varied motion and 2nd Principle of Mechanics formulas, based on mathematical calculation literacy. Discussing the solutions of the solved problems, comparing various results and methods used to obtain them. Possible and / or useful connections to Chemistry and Biology and Sensors Sampling Communications Modules. Might be related to: two Content Units, in 9th grade Physics Curriculum (Principles and laws in classic Mechanics, Variation theorems and Conservation laws in Mechanics); technological disciplines, if available, at curriculum level.
Stakeholder involvement	Independent school activity (general situation). Possible assistance or / and support and connected activities during technical measurements lab classes (in own school or at partner schools) or thematic activities in local Scientific Centres (if available).

EQUIPMENT AND MATERIALS NEEDED

For 1 team of 5 students

Item

Quantity

Remarks

Computers

(in school labs), with Internet access

1-2/team (1/student, if available)

Other available IT equipment can be used (laptops, tablets, mobile phones), with Internet access.

It is a systematization and problem-solving lesson, so it can be organized in a classroom, or in a Physics lab, depending on available facilities.

Virtual measurements labs (if available)

1/team

This is a recommended list:

Observations

In each class / lab, 1-2 blackboards or whiteboards (magnetic and/or interactive), with chalk or markers to write on, will be available.
Teachers will offer students necessary informative and practical support (worksheets, electronic presentations, online thematic images, videos, and tutorials).

STEP-BY-STEP ACTIVITIES
Step 1 (2 min)	Organizational moment (checking presence, capturing attention, preparing didactic materials, etc.)
Step 2 (10 min)	Updating the previous knowledge necessary to solve problems. Students are asked to write the formulas and units of measurement in the International Measurement System, corresponding to the following notions: velocity and relative velocity; acceleration; laws of uniform rectilinear and uniformly varied motions; formula of the 2nd Principle of Dynamics; mechanical impulse; definition of newton, the international unit of measure for force (1 newton of force is the force required to accelerate an object with a mass of 1 kilogram 1 meter per second squared). Energizing exercise: students take turns at the board to complete the table.
Step 3 (25 min)	Fixing and consolidating knowledge through problem solving. The problem-solving activity is directed by following the classic solving steps: problem data notation; transformation of measurement units into International Measurement System units; making an explanatory drawing; suggesting way(s) to solve the problem; requesting the mathematical relationships necessary to perform the literary calculation in order to express the final results; interpretation of the obtained results.
Step 4 (5 min)	Feedback through short questions and answers related to the solved problems, such as: Which problem seemed to you the easiest and which was the hardest? Why? Which problem was more interesting? Why? Which problem was considered to be the most challenging? Why? Filling in a K-W-L (Know-Want to know-Learned) table or diagram (if necessary / applicable).
Step 5 (3 min)	Conclusions: specifying the homework (if necessary / applicable); oral and / or written appreciation (grades) for the students who answered during class.
Assessment	Oral current check Systematic observation of students, working either individually or within their team Evaluation of the results obtained after solving the given problems and the way students were able to present it at the board
Useful links	English: https://study.com/academy/lesson/elements-of-the-si-base-derived-units.html (SI Units \| Base & Derived Units) https://study.com/academy/lesson/speed-velocity-acceleration.html (Speed, Velocity & Acceleration \| Difference & Relationship) https://study.com/learn/lesson/newton-overview-measurement-unit-force.html (Newton Unit \| Overview, Conversion & Examples) https://study.com/academy/lesson/measuring-force-lesson-for-kids.html (Measuring force) https://study.com/academy/lesson/measuring-mass-weight-with-newtons-laws.html (Measuring Mass & Weight With Newton's Laws)

WORKSHEET

Problems referring to the relative movement of boats on a river

On a river that flows at a constant velocity, Vw = 3 m/s, there is a motor boat that can move at a velocity of 9 m/s relative to the water.

For general school and high school students

Statement:

The boat has to travel a distance of 100 m between two trees, A and B, located on the same side of the river. When moving along the river, the boat is oriented parallel to the velocity of the water flow. It is considered that the observer is on the shore, at a fixed point, close to the tree A, and the direction of the water flow is from A to B in relation to this observer.

Notations:

Va – the water flow velocity vector relative to the shore
Vb – the velocity vector of the boat with the engine running against the water

Calculate:

The time in which the boat covers the distance from A to B with the engine off.
The time in which the boat covers the distance from A to B with the engine running.
The time in which the boat covers the distance from B to A with the engine running.
The time in which the boat travels the way back A-B-A with the engine running.

For high school students:

Statement:

The boat has to cross the river, which is 10 m wide to the opposite bank. It is considered that on the opposite bank there is a tree C, located in a way that AC is perpendicular to AB. When crossing the river, the boat is oriented perpendicular to the velocity of the water flow.

Notation:

Vr – the relative velocity vector of the boat

Calculate:

The time required for the boat to cross the river from A to M (located on the opposite bank) with the engine running.
Distance CM on which the boat moves, carried by the current, downstream from point C.

Erasmus+ Cooperation partnerships project

Sailing Into Opportunities

No. 2023-1-LT01-KA220-SCH-000161306

Funded by the European Union. Views and opinions expressed are however those of the author(s) only and do not necessarily reflect those of the European Union or the National Agency. Neither the European Union nor National Agency can be held responsible for them.

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Physics and the movement of boats – problem solving exercises

1. Physics and the movement of boats – problem solving exercises