6.3 Vectors in a Plane
|
|
|
- Madison Lane
- 6 years ago
- Views:
Transcription
1 6.3 Vectors in a Plane Plan: Represent ectors as directed line segments. Write the component form of ectors. Perform basic ector operations and represent ectors graphically. Find the direction angles of ectors. Use ectors to model and sole real-life problems. Homework: P 433 #3-102 (by 3 s) Vectors Used to represent quantities that hae both magnitude and direction. directed line segment terminal point - denotes magnitude or length of the segment initial point 1
2 Vectors Lower case bold letters are used to represent ectors. Two directed line segments (ectors) are equialent if they hae the same magnitude (length) and the same direction. Writing Vectors in Component Form Gien initial point P(p 1, p 2 ) and terminal point Q(q 1, q 2 ) the magnitude (length) of a unit ector has a magnitude of 1. if then is a unit ector 2
3 Writing Vectors in Component Form Examples Gien the initial and terminal points, respectiely #11 #8 Equialent Vectors Hae same length Hae same slope y (0, 4) (3, 3) 1 x (0, 5) 3
4 Vector in Standard Position can be uniquely represent by the coordinates y (2, 5) x Component Form just like an ordered pair but different notation! Zero Vector both the initial and the terminal point are at (0, 0) 0 Vector Operations Scalar Multiplication - k Algebraically k where k is a constant Geometrically 2 4
5 Vector Operations Vector addition-adding two ectors Geometrically Algebraically Gien: u Then: u+ u Examples of Vector Operations Use the figure to sketch a graph of the specified ector: #14 3 #16 u #18 u (1/2) 5
6 Examples of Vector Operations #26 Find u+ u 2u 3 4u gien: u and Properties of Vector Addition These properties are fairly intuitie! 6
7 Unit Vectors a ector with a magnitude of one that is in the same direction as a non-zero ector. unit ector = changed the "scale" to 1 unit! Writing Unit Vectors #40 Standard Unit Vectors i j "i" "j" form y 2 the unit ectors can be used to represent any ector. = 1 i+ 2 j the scalars, 1 and 2 are the horizontal and ertical components of. 1 j = 1 i+ 2 j is called a linear combination. i x 7
8 Writing a Linear Combination write in "i" "j" form Gien the initial and terminal points, respectiely #54 #52 Operations with Vectors in i j form #29 Gien: u= i + j =- 2i-3j find: u+ u- 2u-3 +4u 8
9 Direction Angles We'e seen directions of ectors but we hae not talked about how to measure the direction! Gien: u θ gies direction of the ector How do we determine θ? θ ector Finding Component Form of a Vector = cosθi + sinθj #64 =-4i-7j Finding Direction Angles Find the magnitude and direction of the ector #61 =8(cos135 o i + sin135 o j) = cosθi + sinθj 9
10 Writing Vectors with magnitude and direction #70 #71 and is in the same direction as u= i + 3j = cosθi + sinθj Writing Vectors #76 find the component form of the sum of u and with direction angles θ u and θ. 10
11 Group Challenge #77 Use the Law of Cosines to find the angle α between the ectors. = i + j, w = 2( i - j ) Answer: o Applications of Vectors Resultant Force Find the angle between the forces gien the magnitude of their resultant. ( Hint: Write force 1 as a ector in the direction of the positie x-axis and force 2 as a ector at an angle with the positie x-axis.) #82 Force 1: 3000 pounds Force 2: 1000 pounds Resultant Force: 3750 pounds. 11
12 Applications of Vectors #84 Velocity A gun with a muzzle elocity of 1200 feet per second is fired at an angle of 4 o with the horizontal. find the ertical and horizontal components of the elocity. Applications of Vectors #86 Tension the cranes shown in the figure are lifting an object that weights 20,240 pounds. Find the tension in the cable of each crane. (How much of the 20,240 pounds is each crane lifting?) 12
13 Applications of Vectors #90 Naigation A commercial jet is flying from Miami to Seattle. The Jet's elocity with respect to the air is 580mph (air speed) and its bearing is 332 o. The wind at the altitude of the plane, is blowing from the southwest with a elocity of 60mph. (a) Draw a figure that gies a isual representation of the problem. (b) Write the elocity of the wind as a ector in component form. (c) Write the elocity of the jet relatie to the air as a ector. (d) What is the speed of the jet with respect to the ground (e) What is the true direction of the jet? Mar 27 9:29 AM 13
14 Key Concepts Gien: Initial Point (a 1, b 1 ) and Terminal Point (a 2, b 2 ) Component Form: = a 2 - a 1, b 2 - b 1 = a, b I/J Form (Linear Combination): = ai + bj Magnitude: Direction: V = Mar 27 9:16 AM 14
15 Mar 27 9:19 AM 15
Unit 11: Vectors in the Plane
135 Unit 11: Vectors in the Plane Vectors in the Plane The term ector is used to indicate a quantity (such as force or elocity) that has both length and direction. For instance, suppose a particle moes
Math 144 Activity #9 Introduction to Vectors
144 p 1 Math 144 ctiity #9 Introduction to Vectors Often times you hear people use the words speed and elocity. Is there a difference between the two? If so, what is the difference? Discuss this with your
8.0 Definition and the concept of a vector:
Chapter 8: Vectors In this chapter, we will study: 80 Definition and the concept of a ector 81 Representation of ectors in two dimensions (2D) 82 Representation of ectors in three dimensions (3D) 83 Operations
27 ft 3 adequately describes the volume of a cube with side 3. ft F adequately describes the temperature of a person.
VECTORS The stud of ectors is closel related to the stud of such phsical properties as force, motion, elocit, and other related topics. Vectors allow us to model certain characteristics of these phenomena
1.1 Vectors. The length of the vector AB from A(x1,y 1 ) to B(x 2,y 2 ) is
1.1 Vectors A vector is a quantity that has both magnitude and direction. Vectors are drawn as directed line segments and are denoted by boldface letters a or by a. The magnitude of a vector a is its length,
2-9. The plate is subjected to the forces acting on members A and B as shown. If θ = 60 o, determine the magnitude of the resultant of these forces
2-9. The plate is subjected to the forces acting on members A and B as shown. If θ 60 o, determine the magnitude of the resultant of these forces and its direction measured clockwise from the positie x
Note: the net distance along the path is a scalar quantity its direction is not important so the average speed is also a scalar.
PHY 309 K. Solutions for the first mid-term test /13/014). Problem #1: By definition, aerage speed net distance along the path of motion time. 1) ote: the net distance along the path is a scalar quantity
Find the component form of with initial point A(1, 3) and terminal point B(1, 3). Component form = 1 1, 3 ( 3) (x 1., y 1. ) = (1, 3) = 0, 6 Subtract.
Express a Vector in Component Form Find the component form of with initial point A(1, 3) and terminal point B(1, 3). = x 2 x 1, y 2 y 1 Component form = 1 1, 3 ( 3) (x 1, y 1 ) = (1, 3) and ( x 2, y 2
Physics 2A Chapter 3 - Motion in Two Dimensions Fall 2017
These notes are seen pages. A quick summary: Projectile motion is simply horizontal motion at constant elocity with ertical motion at constant acceleration. An object moing in a circular path experiences
6.1.1 Angle between Two Lines Intersection of Two lines Shortest Distance from a Point to a Line
CHAPTER 6 : VECTORS 6. Lines in Space 6.. Angle between Two Lines 6.. Intersection of Two lines 6..3 Shortest Distance from a Point to a Line 6. Planes in Space 6.. Intersection of Two Planes 6.. Angle
u + v = u - v =, where c Directed Quantities: Quantities such as velocity and acceleration (quantities that involve magnitude as well as direction)
Pre-Calculus Section 10.3: Vectors & Their Applications (Part I) 1. Vocabulary (Summary): 4. Algebraic Operations on Vectors: If u = Scalar: A quantity possessing only magnitude (such weight or length
UNDERSTAND MOTION IN ONE AND TWO DIMENSIONS
SUBAREA I. COMPETENCY 1.0 UNDERSTAND MOTION IN ONE AND TWO DIMENSIONS MECHANICS Skill 1.1 Calculating displacement, aerage elocity, instantaneous elocity, and acceleration in a gien frame of reference
Section 10.4 Vectors
220 Section 10.4 Vectors In this section, we will define and explore the properties of vectors. Vectors can be used to represent the speed and the direction of an object, the force and direction acting
12.1 Three Dimensional Coordinate Systems (Review) Equation of a sphere
12.2 Vectors 12.1 Three Dimensional Coordinate Systems (Reiew) Equation of a sphere x a 2 + y b 2 + (z c) 2 = r 2 Center (a,b,c) radius r 12.2 Vectors Quantities like displacement, elocity, and force inole
The Dot Product Pg. 377 # 6ace, 7bdf, 9, 11, 14 Pg. 385 # 2, 3, 4, 6bd, 7, 9b, 10, 14 Sept. 25
UNIT 2 - APPLICATIONS OF VECTORS Date Lesson TOPIC Homework Sept. 19 2.1 (11) 7.1 Vectors as Forces Pg. 362 # 2, 5a, 6, 8, 10 13, 16, 17 Sept. 21 2.2 (12) 7.2 Velocity as Vectors Pg. 369 # 2,3, 4, 6, 7,
different formulas, depending on whether or not the vector is in two dimensions or three dimensions.
ectors The word ector comes from the Latin word ectus which means carried. It is best to think of a ector as the displacement from an initial point P to a terminal point Q. Such a ector is expressed as
Vector Supplement Part 1: Vectors
Vector Supplement Part 1: Vectors A vector is a quantity that has both magnitude and direction. Vectors are drawn as directed line segments and are denoted by boldface letters a or by a. The magnitude
sin! =! d y =! d T ! d y = 15 m = m = 8.6 m cos! =! d x ! d x ! d T 2 =! d x 2 +! d y =! d x 2 +! d y = 27.2 m = 30.0 m tan! =!
Section. Motion in Two Dimensions An Algebraic Approach Tutorial 1 Practice, page 67 1. Gien d 1 = 7 m [W]; d = 35 m [S] Required d T Analysis d T = d 1 + d Solution Let φ represent the angle d T with
(a) Taking the derivative of the position vector with respect to time, we have, in SI units (m/s),
Chapter 4 Student Solutions Manual. We apply Eq. 4- and Eq. 4-6. (a) Taking the deriatie of the position ector with respect to time, we hae, in SI units (m/s), d ˆ = (i + 4t ˆj + tk) ˆ = 8tˆj + k ˆ. dt
Vectors are used to represent quantities such as force and velocity which have both. and. The magnitude of a vector corresponds to its.
Fry Texas A&M University Fall 2016 Math 150 Notes Chapter 9 Page 248 Chapter 9 -- Vectors Remember that is the set of real numbers, often represented by the number line, 2 is the notation for the 2-dimensional
Blue and purple vectors have same magnitude and direction so they are equal. Blue and green vectors have same direction but different magnitude.
A ector is a quantity that has both magnitude and direction. It is represented by an arrow. The length of the ector represents the magnitude and the arrow indicates the direction of the ector. Blue and
CHAPTER 3 : VECTORS. Definition 3.1 A vector is a quantity that has both magnitude and direction.
EQT 101-Engineering Mathematics I Teaching Module CHAPTER 3 : VECTORS 3.1 Introduction Definition 3.1 A ector is a quantity that has both magnitude and direction. A ector is often represented by an arrow
OpenStax-CNX module: m Vectors. OpenStax College. Abstract
OpenStax-CNX module: m49412 1 Vectors OpenStax College This work is produced by OpenStax-CNX and licensed under the Creative Commons Attribution License 4.0 In this section you will: Abstract View vectors
VECTORS. Section 6.3 Precalculus PreAP/Dual, Revised /11/ :41 PM 6.3: Vectors in the Plane 1
VECTORS Section 6.3 Precalculus PreAP/Dual, Revised 2017 Viet.dang@humbleisd.net 10/11/2018 11:41 PM 6.3: Vectors in the Plane 1 DEFINITIONS A. Vector is used to indicate a quantity that has both magnitude
Math 20C. Lecture Examples.
Math 20C. Lecture Eamples. (8//08) Section 2.. Vectors in the plane Definition A ector represents a nonnegatie number and, if the number is not zero, a direction. The number associated ith the ector is
Vectors in the Plane
Vectors in the Plane MATH 311, Calculus III J. Robert Buchanan Department of Mathematics Fall 2011 Vectors vs. Scalars scalar quantity having only a magnitude (e.g. temperature, volume, length, area) and
Appendix D: Algebra and Trig Review
Appendix D: Algebra and Trig Review Find the domains of the following functions. x+2 x 2 5x+4 3 x 4 + x 2 9 7 x If f(x) = x 3, find f(8+h) f(8) h and simplify by rationalizing the numerator. 1 Converting
Chapter 6 Additional Topics in Trigonometry
Chapter 6 Additional Topics in Trigonometry Overview: 6.1 Law of Sines 6.2 Law of Cosines 6.3 Vectors in the Plan 6.4 Vectors and Dot Products 6.1 Law of Sines What You ll Learn: #115 - Use the Law of
Vectors in R n. P. Danziger
1 Vectors in R n P. Danziger 1 Vectors The standard geometric definition of ector is as something which has direction and magnitude but not position. Since ectors hae no position we may place them whereer
Geostrophy & Thermal wind
Lecture 10 Geostrophy & Thermal wind 10.1 f and β planes These are planes that are tangent to the earth (taken to be spherical) at a point of interest. The z ais is perpendicular to the plane (anti-parallel
DO PHYSICS ONLINE. WEB activity: Use the web to find out more about: Aristotle, Copernicus, Kepler, Galileo and Newton.
DO PHYSICS ONLINE DISPLACEMENT VELOCITY ACCELERATION The objects that make up space are in motion, we moe, soccer balls moe, the Earth moes, electrons moe, - - -. Motion implies change. The study of the
Congruence Axioms. Data Required for Solving Oblique Triangles
Math 335 Trigonometry Sec 7.1: Oblique Triangles and the Law of Sines In section 2.4, we solved right triangles. We now extend the concept to all triangles. Congruence Axioms Side-Angle-Side SAS Angle-Side-Angle
The polar coordinates of a point are given. Find the rectangular coordinates of the point. 1) 7, 2 3 D) - 7 2, A) - 7 2, 7 3
Ch 9. Assignment Name MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. The polar coordinates of a point are given. Find the rectangular coordinates
Space Coordinates and Vectors in Space. Coordinates in Space
0_110.qd 11//0 : PM Page 77 SECTION 11. Space Coordinates and Vectors in Space 77 -plane Section 11. -plane -plane The three-dimensional coordinate sstem Figure 11.1 Space Coordinates and Vectors in Space
Chapter 6. Additional Topics in Trigonometry. 6.6 Vectors. Copyright 2014, 2010, 2007 Pearson Education, Inc.
Chapter 6 Additional Topics in Trigonometry 6.6 Vectors Copyright 2014, 2010, 2007 Pearson Education, Inc. 1 Obectives: Use magnitude and direction to show vectors are equal. Visualize scalar multiplication,
Physics 4A Solutions to Chapter 4 Homework
Physics 4A Solutions to Chapter 4 Homework Chapter 4 Questions: 4, 1, 1 Exercises & Problems: 5, 11, 3, 7, 8, 58, 67, 77, 87, 11 Answers to Questions: Q 4-4 (a) all tie (b) 1 and tie (the rocket is shot
Motion In Two Dimensions. Vectors in Physics
Motion In Two Dimensions RENE DESCARTES (1736-1806) GALILEO GALILEI (1564-1642) Vectors in Physics All physical quantities are either scalars or ectors Scalars A scalar quantity has only magnitude. In
Chapter 1E - Complex Numbers
Fry Texas A&M University Math 150 Spring 2015 Unit 4 20 Chapter 1E - Complex Numbers 16 exists So far the largest (most inclusive) number set we have discussed and the one we have the most experience with
Chapter 6 Additional Topics in Trigonometry, Part II
Chapter 6 Additional Topics in Trigonometry, Part II Section 3 Section 4 Section 5 Vectors in the Plane Vectors and Dot Products Trigonometric Form of a Complex Number Vocabulary Directed line segment
θ Vman V ship α φ V β
Answer, Key { Homework 3 { Rubin H Landau 1 This print-out should hae 9 uestions. Check that it is complete before leaing the printer. Also, multiple-choice uestions may continue on the next column or
VIII - Geometric Vectors
MTHEMTIS 0-NY-05 Vectors and Matrices Martin Huard Fall 07 VIII - Geometric Vectors. Find all ectors in the following parallelepiped that are equialent to the gien ectors. E F H G a) b) c) d) E e) f) F
Linear Momentum and Collisions Conservation of linear momentum
Unit 4 Linear omentum and Collisions 4.. Conseration of linear momentum 4. Collisions 4.3 Impulse 4.4 Coefficient of restitution (e) 4.. Conseration of linear momentum m m u u m = u = u m Before Collision
Motion in Two and Three Dimensions
PH 1-1D Spring 013 Motion in Two and Three Dimensions Lectures 5,6,7 Chapter 4 (Halliday/Resnick/Walker, Fundamentals of Physics 9 th edition) 1 Chapter 4 Motion in Two and Three Dimensions In this chapter
3. What is the minimum work needed to push a 950-kg car 310 m up along a 9.0 incline? Ignore friction. Make sure you draw a free body diagram!
Wor Problems Wor and Energy HW#. How much wor is done by the graitational force when a 280-g pile drier falls 2.80 m? W G = G d cos θ W = (mg)d cos θ W = (280)(9.8)(2.80) cos(0) W = 7683.2 W 7.7 0 3 Mr.
Chapter 11 Collision Theory
Chapter Collision Theory Introduction. Center o Mass Reerence Frame Consider two particles o masses m and m interacting ia some orce. Figure. Center o Mass o a system o two interacting particles Choose
Lesson 3: Free fall, Vectors, Motion in a plane (sections )
Lesson 3: Free fall, Vectors, Motion in a plane (sections.6-3.5) Last time we looked at position s. time and acceleration s. time graphs. Since the instantaneous elocit is lim t 0 t the (instantaneous)
LECTURE 2: CROSS PRODUCTS, MULTILINEARITY, AND AREAS OF PARALLELOGRAMS
LECTURE : CROSS PRODUCTS, MULTILINEARITY, AND AREAS OF PARALLELOGRAMS MA1111: LINEAR ALGEBRA I, MICHAELMAS 016 1. Finishing up dot products Last time we stated the following theorem, for which I owe you
Vectors and the Geometry of Space
Vectors and the Geometr of Space. Vectors in the Plane. Space Coordinates and Vectors in Space. The Dot Product of Two Vectors. The Cross Product of Two Vectors in Space.5 Lines and Planes in Space.6 Surfaces
C) ) cos (cos-1 0.4) 5) A) 0.4 B) 2.7 C) 0.9 D) 3.5 C) - 4 5
Precalculus B Name Please do NOT write on this packet. Put all work and answers on a separate piece of paper. MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the
1 Vectors. c Kun Wang. Math 151, Fall Vector Supplement
Vector Supplement 1 Vectors A vector is a quantity that has both magnitude and direction. Vectors are drawn as directed line segments and are denoted by boldface letters a or by a. The magnitude of a vector
Chapter 1: Kinematics of Particles
Chapter 1: Kinematics of Particles 1.1 INTRODUCTION Mechanics the state of rest of motion of bodies subjected to the action of forces Static equilibrium of a body that is either at rest or moes with constant
A vector in the plane is directed line segment. The directed line segment AB
Vector: A ector is a matrix that has only one row then we call the matrix a row ector or only one column then we call it a column ector. A row ector is of the form: a a a... A column ector is of the form:
Name: Date: Practice Midterm Exam Sections 1.2, 1.3, , ,
Name: Date: Practice Midterm Exam Sections 1., 1.3,.1-.7, 6.1-6.5, 8.1-8.7 a108 Please develop your one page formula sheet as you try these problems. If you need to look something up, write it down on
When two letters name a vector, the first indicates the and the second indicates the of the vector.
8-8 Chapter 8 Applications of Trigonometry 8.3 Vectors, Operations, and the Dot Product Basic Terminology Algeraic Interpretation of Vectors Operations with Vectors Dot Product and the Angle etween Vectors
Vectors are used to represent quantities such as force and velocity which have both. and. The magnitude of a vector corresponds to its.
Fry Texas A&M University Math 150 Chapter 9 Fall 2014 1 Chapter 9 -- Vectors Remember that is the set of real numbers, often represented by the number line, 2 is the notation for the 2-dimensional plane.
11.4 Dot Product Contemporary Calculus 1
11.4 Dot Product Contemporary Calculus 1 11.4 DOT PRODUCT In the previous sections we looked at the meaning of vectors in two and three dimensions, but the only operations we used were addition and subtraction
PreCalculus Second Semester Review Chapters P-3(1st Semester)
PreCalculus Second Semester Review Chapters P-(1st Semester) Solve. Check for extraneous roots. All but #15 from 1 st semester will be non-calculator. P 1. x x + 5 = 1.8. x x + x 0 (express the answer
Chapter 7.4: Vectors
Chapter 7.4: Vectors In many mathematical applications, quantities are determined entirely by their magnitude. When calculating the perimeter of a rectangular field, determining the weight of a box, or
FOCUS ON CONCEPTS Section 7.1 The Impulse Momentum Theorem
WEEK-6 Recitation PHYS 3 FOCUS ON CONCEPTS Section 7. The Impulse Momentum Theorem Mar, 08. Two identical cars are traeling at the same speed. One is heading due east and the other due north, as the drawing
Unit #17: Spring Trig Unit. A. First Quadrant Notice how the x-values decrease by while the y-values increase by that same amount.
Name Unit #17: Spring Trig Unit Notes #1: Basic Trig Review I. Unit Circle A circle with center point and radius. A. First Quadrant Notice how the x-values decrease by while the y-values increase by that
Motion in Two and Three Dimensions
PH 1-A Fall 014 Motion in Two and Three Dimensions Lectures 4,5 Chapter 4 (Halliday/Resnick/Walker, Fundamentals of Physics 9 th edition) 1 Chapter 4 Motion in Two and Three Dimensions In this chapter
PreCalculus Notes. MAT 129 Chapter 10: Polar Coordinates; Vectors. David J. Gisch. Department of Mathematics Des Moines Area Community College
PreCalculus Notes MAT 129 Chapter 10: Polar Coordinates; Vectors David J. Gisch Department of Mathematics Des Moines Area Community College October 25, 2011 1 Chapter 10 Section 10.1: Polar Coordinates
Chapter 8: Polar Coordinates and Vectors
Chapter 8: Polar Coordinates and Vectors 8.1 Polar Coordinates This is another way (in addition to the x-y system) of specifying the position of a point in the plane. We give the distance r of the point
Announcements Wednesday, September 06. WeBWorK due today at 11:59pm. The quiz on Friday covers through Section 1.2 (last weeks material)
Announcements Wednesday, September 06 WeBWorK due today at 11:59pm. The quiz on Friday coers through Section 1.2 (last eeks material) Announcements Wednesday, September 06 Good references about applications(introductions
Day 1: Introduction to Vectors + Vector Arithmetic
Day 1: Introduction to Vectors + Vector Arithmetic A is a quantity that has magnitude but no direction. You can have signed scalar quantities as well. A is a quantity that has both magnitude and direction.
Feb 6, 2013 PHYSICS I Lecture 5
95.141 Feb 6, 213 PHYSICS I Lecture 5 Course website: faculty.uml.edu/pchowdhury/95.141/ www.masteringphysics.com Course: UML95141SPRING213 Lecture Capture h"p://echo36.uml.edu/chowdhury213/physics1spring.html
8-2 Vectors in the Coordinate Plane
37. ROWING Nadia is rowing across a river at a speed of 5 miles per hour perpendicular to the shore. The river has a current of 3 miles per hour heading downstream. a. At what speed is she traveling? b.
CJ57.P.003 REASONING AND SOLUTION According to the impulse-momentum theorem (see Equation 7.4), F t = mv
Solution to HW#7 CJ57.CQ.003. RASONNG AND SOLUTON a. Yes. Momentum is a ector, and the two objects hae the same momentum. This means that the direction o each object s momentum is the same. Momentum is
9.1 VECTORS. A Geometric View of Vectors LEARNING OBJECTIVES. = a, b
vectors and POLAR COORDINATES LEARNING OBJECTIVES In this section, ou will: View vectors geometricall. Find magnitude and direction. Perform vector addition and scalar multiplication. Find the component
Chapter 5 Solution P5.2-2, 3, 6 P5.3-3, 5, 8, 15 P5.4-3, 6, 8, 16 P5.5-2, 4, 6, 11 P5.6-2, 4, 9
Chapter 5 Solution P5.2-2, 3, 6 P5.3-3, 5, 8, 15 P5.4-3, 6, 8, 16 P5.5-2, 4, 6, 11 P5.6-2, 4, 9 P 5.2-2 Consider the circuit of Figure P 5.2-2. Find i a by simplifying the circuit (using source transformations)
Test # 3 Review Math Name (6.5 to 6.7, 10.1 to 10.3,and 10.5)
Test # Review Math 14 Name (6.5 to 6.7, 10.1 to 10.,and 10.5) Date: MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Find the product of the complex
A Geometric Review of Linear Algebra
A Geometric Reiew of Linear Algebra The following is a compact reiew of the primary concepts of linear algebra. The order of presentation is unconentional, with emphasis on geometric intuition rather than
BELLWORK feet
BELLWORK 1 A hot air balloon is being held in place by two people holding ropes and standing 35 feet apart. The angle formed between the ground and the rope held by each person is 40. Determine the length
Pearson Physics Level 20 Unit I Kinematics: Chapter 2 Solutions
Pearson Phsics Leel 0 Unit I Kinematics: Chapter Solutions Student Book page 71 Skills Practice Students answers will ar but ma consist of: (a) scale 1 cm : 1 m; ector will be 5 cm long scale 1 m forward
Doppler shifts in astronomy
7.4 Doppler shift 253 Diide the transformation (3.4) by as follows: = g 1 bck. (Lorentz transformation) (7.43) Eliminate in the right-hand term with (41) and then inoke (42) to yield = g (1 b cos u). (7.44)
VISUAL PHYSICS ONLINE RECTLINEAR MOTION: UNIFORM ACCELERATION
VISUAL PHYSICS ONLINE RECTLINEAR MOTION: UNIFORM ACCELERATION Predict Obsere Explain Exercise 1 Take an A4 sheet of paper and a heay object (cricket ball, basketball, brick, book, etc). Predict what will
Dynamics ( 동역학 ) Ch.2 Motion of Translating Bodies (2.1 & 2.2)
Dynamics ( 동역학 ) Ch. Motion of Translating Bodies (. &.) Motion of Translating Bodies This chapter is usually referred to as Kinematics of Particles. Particles: In dynamics, a particle is a body without
Scalar multiplication and algebraic direction of a vector
Roberto s Notes on Linear Algebra Chapter 1: Geometric ectors Section 5 Scalar multiplication and algebraic direction of a ector What you need to know already: of a geometric ectors. Length and geometric
Chapter 2: 1D Kinematics Tuesday January 13th
Chapter : D Kinematics Tuesday January 3th Motion in a straight line (D Kinematics) Aerage elocity and aerage speed Instantaneous elocity and speed Acceleration Short summary Constant acceleration a special
DEVIL PHYSICS THE BADDEST CLASS ON CAMPUS AP PHYSICS
DEVIL PHYSICS THE BADDEST CLASS ON CAMPUS AP PHYSICS LSN 3-7: PROJECTILE MOTION IS PARABOLIC LSN 3-8: RELATIVE VELOCITY Questions From Reading Actiity? Big Idea(s): The interactions of an object with other
Applications of Forces
Chapter 10 Applications of orces Practice Problem Solutions Student Textbook page 459 1. (a) rame the Problem - Make a sketch of the ector. - The angle is between 0 and 90 so it is in the first quadrant.
a by a factor of = 294 requires 1/T, so to increase 1.4 h 294 = h
IDENTIFY: If the centripetal acceleration matches g, no contact force is required to support an object on the spinning earth s surface. Calculate the centripetal (radial) acceleration /R using = πr/t to
SB Ch 6 May 15, 2014
Warm Up 1 Chapter 6: Applications of Trig: Vectors Section 6.1 Vectors in a Plane Vector: directed line segment Magnitude is the length of the vector Direction is the angle in which the vector is pointing
A-level Mathematics. MM03 Mark scheme June Version 1.0: Final
-leel Mathematics MM0 Mark scheme 660 June 0 Version.0: Final Mark schemes are prepared by the Lead ssessment Writer and considered, together with the releant questions, by a panel of subject teachers.
9.4 Polar Coordinates
9.4 Polar Coordinates Polar coordinates uses distance and direction to specify a location in a plane. The origin in a polar system is a fixed point from which a ray, O, is drawn and we call the ray the
Quadratic Equation. ax bx c =. = + + =. Example 2. = + = + = 3 or. The solutions are -7/3 and 1.
Quadratic Equation A quadratic equation is any equation that is equialent to the equation in fmat a c + + = 0 (1.1) where a,, and c are coefficients and a 0. The ariale name is ut the same fmat applies
Bonus Section II: Solving Trigonometric Equations
Fry Texas A&M University Math 150 Spring 2017 Bonus Section II 260 Bonus Section II: Solving Trigonometric Equations (In your text this section is found hiding at the end of 9.6) For what values of x does
Chapter 3 2-D Motion
Chapter 3 2-D Motion We will need to use vectors and their properties a lot for this chapter. .. Pythagorean Theorem: Sample problem: First you hike 100 m north. Then hike 50 m west. Finally
Chapter 3 Motion in a Plane
Chapter 3 Motion in a Plane Introduce ectors and scalars. Vectors hae direction as well as magnitude. The are represented b arrows. The arrow points in the direction of the ector and its length is related
A unit vector in the same direction as a vector a would be a and a unit vector in the
In the previous lesson we discussed unit vectors on the positive x-axis (i) and on the positive y- axis (j). What is we wanted to find other unit vectors? There are an infinite number of unit vectors in
BC VECTOR PROBLEMS. 13. Find the area of the parallelogram having AB and AC as adjacent sides: A(2,1,3), B(1,4,2), C( 3,2,7) 14.
For problems 9 use: u (,3) v (3, 4) s (, 7). w =. 3u v = 3. t = 4. 7u = u w (,3,5) 5. wt = t (,, 4) 6. Find the measure of the angle between w and t to the nearest degree. 7. Find the unit vector having
u P(t) = P(x,y) r v t=0 4/4/2006 Motion ( F.Robilliard) 1
y g j P(t) P(,y) r t0 i 4/4/006 Motion ( F.Robilliard) 1 Motion: We stdy in detail three cases of motion: 1. Motion in one dimension with constant acceleration niform linear motion.. Motion in two dimensions
MOTION IN 2-DIMENSION (Projectile & Circular motion And Vectors)
MOTION IN -DIMENSION (Projectile & Circular motion nd Vectors) INTRODUCTION The motion of an object is called two dimensional, if two of the three co-ordinates required to specif the position of the object
Mon Apr dot product, length, orthogonality, projection onto the span of a single vector. Announcements: Warm-up Exercise:
Math 2270-004 Week 2 notes We will not necessarily finish the material from a gien day's notes on that day. We may also add or subtract some material as the week progresses, but these notes represent an
Would you risk your live driving drunk? Intro
Martha Casquete Would you risk your lie driing drunk? Intro Motion Position and displacement Aerage elocity and aerage speed Instantaneous elocity and speed Acceleration Constant acceleration: A special
CHAPTER 3: Kinematics in Two Dimensions; Vectors
HAPTER 3: Kinematics in Two Dimensions; Vectors Solution Guide to WebAssign Problems 3.1 [] The truck has a displacement of 18 + (16) blocks north and 1 blocks east. The resultant has a magnitude of +
(a) During the first part of the motion, the displacement is x 1 = 40 km and the time interval is t 1 (30 km / h) (80 km) 40 km/h. t. (2.
Chapter 3. Since the trip consists of two parts, let the displacements during first and second parts of the motion be x and x, and the corresponding time interals be t and t, respectiely. Now, because
Status: Unit 2, Chapter 3
1 Status: Unit, Chapter 3 Vectors and Scalars Addition of Vectors Graphical Methods Subtraction of Vectors, and Multiplication by a Scalar Adding Vectors by Components Unit Vectors Vector Kinematics Projectile
PreCalculus: Chapter 9 Test Review
Name: Class: Date: ID: A PreCalculus: Chapter 9 Test Review Short Answer 1. Plot the point given in polar coordinates. 3. Plot the point given in polar coordinates. (-4, -225 ) 2. Plot the point given
Physics Department Tutorial: Motion in a Circle (solutions)
JJ 014 H Physics (9646) o Solution Mark 1 (a) The radian is the angle subtended by an arc length equal to the radius of the circle. Angular elocity ω of a body is the rate of change of its angular displacement.