VECTORS: Traveling, But in What Direction (Grades 9-12)
The trigonometric ratios have many applications in physics, some of which you will learn in a-lis lesson. This lesson concems vectors. Vectors are entities, such as velocity and force, which require both magnitude and direction for their description. Graphically, we may think of a vector as an arrow whose length represents the magnitude of the vector and angle with reference line represents its direction. The video will show students how to draw vectors and use the trigonometric ratios to find the resultant force. This lesson will provide students with the opportunity to use mathematics and science in real-life problem solving situations.
Vectors, Lesson 1: Follow
Vectors, Lesson 2: Finding the Resultant
Students will be able to
- draw and use vectors to solve problems
- find the magnitude and direction of a vector
- use trigonometric ratios to solve problems that involve right triangles
- grid paper
SC-MATH/SCIENCE STANDARDS MET
Science Achievement Standards Process Skills Measure
- Use scientific notation, exponents, significant digits, and metric units/or SI units.
- Estimate using metric and/or SI units.
Make inferences based on direct and indirect observations using prior knowledge and/or experiences.
- Design, conduct, and evaluate a scientific investigation Use advanced technologies to extend investigations
- Use technology (calculators, computers, etc.) to collect, catalo& and graphically represent data
Communicate and defend scientific thinking that leads
Matter and Energy Area III Strand 1
- Investigate and analyze characteristics of motion and the net result of applied forces by using mathematical equations, graphs, and vectors diagrams to describe them.
- Describe motion of an object by its position, direction, and speed and acceleration.
- Translate a description of a physical problem into a mathematical equation to solve.
- Analyze the relationship of displacement, time, rate of motion, and rate of change of motion.
- Mustrate rate and change in motion mathematically and graphically.
Mathematics Academic Achievement Standards Patterns, Relationships, and Functions Translate among tabular, symbolic, and graphical representations of functions, using technology whenever appropriate by:
Using graphs to determine the value of one variable from the value of the other.
Describing and analyzing the behavior of the graph of a function.
Use technology whenever appropriate to explore concepts and applications of geometry by:
- Applying the Pythagorean theorem to solve real-world problems.
Apply trigonometry to problem situations involving triangles by:
- Using the sine, cosine, and tangent ratios to solve problems, using technology whenever appropriate.
Explore periodic real-world phenomena using the sine and cosine functions by:
- Using technology to apply the sine and cosine functions to repetitive physical phenomena such as ocean tides, sound waves, and electric current.
Estimate, construct, and use measurement for descriptions and comparison by:
- Constructing an object or figure according to specific measuring requirements.
- Choosing appropriate techniques, units, and tools to measure quantities.
- Converting units of measure within a system to solve problems that involve various measurement units, using technology whenever appropriate.
Connect measurement to other aspects of mathematics and other disciplines by:
- Using technology to explore concepts of measurement.
Tell the students that vectors for a
general case are defined by indicating the two properties
of magnitude and direction. Draw several examples of
Have the students give examples of signed numbers and vectors from their experiences. Ask them how does using signed numbers and vectors make life easier?
FOCUS FOR VIEWING
Give the students a series of questions to answer as they view the video tape. Tell them that they will be asked throughout the tape the answers to the questions. Tell them that they will do a video problem.
Pass out Activity Sheet 1. Begin the tape where the two cars meet and tell the students to listen carefully for the answers to the questions. Stop the tape at the word "temperature" and ask the first three questions on Activity Sheet 1. After the questions have been answered, begin the tape and stop the tape when you see "9m", then ask the next four questions. Fast forward the tape to where the car is in the water and ask the, last series of questions except the video problem. Stop the tape after the speed and direction are given for the airplane and have students complete the video problem. Begin the tape after the students have solved the problem so that they will see the explanation then stop tape.
Activity Sheet 2. Students will use a protractor to draw the angle measure of a vector. They will find the magnitude and direction of a vector by using a calculator. They will use the trigonometric ratios to find the resultant force.