Chapter 3. Vectors. θ that the vector forms with i ˆ is 15. I. Vectors and Scalars
|
|
- John Allison
- 6 years ago
- Views:
Transcription
1 Chapter 3. Vectors I. Vectors and Scalars 1. What type of quantity does the odometer of a car measure? a) vector; b) scalar; c) neither scalar nor vector; d) both scalar and vector. 2. What type of quantity does the speedometer of a car measure? a) vector; b) scalar; c) neither scalar not vector; d) both scalar and vector. 3. Which of the following is a vector? a) mass; b) temperature; c) speed; d) acceleration; e) time. 4. During baseball practice, a batter hits a very high fly ball, and then runs in a straight line and catches it. When comparing the displacement for the two, one sees that the? a) player's displacement is larger; b) ball's displacement is larger; c) two displacements are equal. 5. Which of the following is a scalar? a) mass; b) displacement; c) velocity; d) acceleration; e) force. II. Components of Vectors 1. Convert α = 54 to radians Convert β = π to degrees Find the î ( ĵ ) component of the vector a r if its magnitude is 15 m and the angle θ that the vector forms with i ˆ is 15 o. 1
2 4. An airplane is taking off with the speed of 600 km/h. Its path is linear, and it makes an angle of 17 o with the horizontal. Assuming that the speed of the airplane remains constant, find the horizontal distance that the airplane travels in 3.5 s. 5. A 12-meter ladder that stands against a wall makes an angle of 50 o with the floor. If a worker gets all the way on top of the ladder, what is the vertical distance he travels? 6. Two vectors a r and b r r are given: a = (1.2 m) iˆ+ (3.0 m) ˆj and r ˆ r r b = ( 1.0 m) i + (2. 7 m) ĵ. Find the magnitude of c = a+ b r. r r r 7. Such vectors a and b are given that a = (4.0 m) iˆ+ (6.3 m) ˆj and r ˆ r r b = (6.0 m) i + (4.9m) ĵ. Find the direction of vector c = a b r in degrees relative to i ˆ. III. Adding and Subtracting Vectors Graphically 1. Two vectors A and B are given. What would be the resultant vector C if A and B are added together? a) c) e) Hint 1/ Vectors can be added graphically without decomposing the vectors into vertical and horizontal components. In order to add the two vectors graphically, place the tail of the vector B at the head of the vector A. The resultant vector (vector C) can be found by drawing a vector from the tail of vector A to the head of vector B. 2
3 2. Two vectors A and B are given. Find C = A B. a) c) e) Hint 1/ Vectors can be added graphically without decomposing the vectors into vertical and horizontal components. Hint 2/ In order to subtract the two vectors graphically, treat the subtraction as addition of a negative vector A B = A + (-B). The negative vector can be represented as an arrow with the same magnitude as the original but pointing in the opposite direction. Place the tail of the vector B at the head of the vector A. The resultant vector (vector C) can be found by drawing a vector from the tail of the vector A to the head of the vector B. 3. Given three vectors A, B and C, find D = A + B + C. 3
4 a) c) e) Hint 1/ Vectors can be added graphically without decomposing the vectors into vertical and horizontal components. In order to add the three vectors graphically, place the tail of the vector B at the head of the vector A, then place the tail of the vector C at the head of the vector B. The resultant vector (vector D) can be found by drawing a vector from the tail of vector A to the head of vector C. 4. Given three vectors A, B and C, find D = A - B + C. a) c) e) Hint 1/ Vectors can be added graphically without decomposing the vectors into vertical and horizontal components. Hint 2/ In order to subtract two vectors graphically, treat the subtraction as addition of a negative vector A B = A + (-B). The negative vector can be represented as an arrow with the same magnitude as the original but pointing in the opposite direction. In order to find D = A - B + C, place the tail of the vector B at the head of the vector A, then place the tail of the vector C at the head of the vector B. The resultant vector (vector D) can be found by drawing a vector from the tail of vector A to the head of vector C. 4
5 5. Given four vectors A, B, C and D, find E = 2A + 2B + C + D. a) c) e) Hint 1/ Vectors can be added graphically without decomposing the vectors into vertical and horizontal components. Hint 2/ Vectors 2A and 2B can be represented graphically as arrows having twice the length of the respective original vectors (vectors A and B). In order to find E = 2A + 2B + C + D, place the tail of the vector 2B at the head of the vector 2A, then place the tail of the vector C at the head of the vector 2B. After that place the tail of the vector D at the head of the vector C. The resultant vector (vector E) can be found by drawing a vector from the tail of vector A to the head of vector D. IV. Position, Displacement and Velocity Vectors. 1. Find the magnitude of the displacement of a truck (car, motorcycle) that traveled 130 mi east and then 50 mi west. Assume that the x-axis is directed east. Hint 1/ Given the direction of motion and the distance that the object moved in that direction, draw two collinear vectors that describe the motion. 5
6 Suppose that the vector A illustrates the object s motion eastward, and the vector B illustrates the motion westward. The picture below shows vector C as the sum of vectors A and B (assuming that the magnitude of the vector A is greater than that of the vector B). 2. An airplane is flying straight north with the speed of 560 km/h. The wind that begins to blow east (from the west) has a speed of 35 km/h. Find the resultant speed (the direction of the resultant velocity vector relative to east) of the airplane. Assume that the x-axis is directed east, and the y-axis is directed north. Hint 1/ Given the magnitudes and directions of the vectors, you can draw the described vectors. Hint 2/ Suppose that vector A represents the velocity of the airplane and vector B represents the velocity of the wind. The picture below shows the resultant vector (vector C). Note that the three vectors form a right triangle. Use Pythagorean theorem to find the magnitude of the resultant velocity vector (vector C). Angle θ specifies the direction of the resultant velocity vector of the airplane relative to east. θ = 90 o α, where α = tan -1 (B/A). 3. A camp of rock climbers is located at point A. Early in the morning, the rock climbers travel 500 m to point B, the base of the cliff, then they climb straight up for 100 m and reach point C. What is the degree measure of angle θ, the angle that the displacement vector s r makes with the horizontal? 6
7 Use trigonometric functions to find the direction of the resultant displacement vector S: θ = tan -1 (BC/AB). 4. A motorcycle is ridden (car is driven) 12 km north, 15 km west, and then 4 km north. What is the magnitude of the displacement from the point of origin? Hint 1/ Given the magnitudes and directions of the vectors, you can draw the described vectors. Hint 2/ Add the two vectors in the north direction together and treat them as one vector. Suppose that vector A represents the two vectors directed north and that vector B represents the displacement vector directed west. Then C is the resultant displacement vector (derived by adding vectors A and B graphically). Vectors A, B, and C form a right triangle, so Pythagorean theorem can be used to find the magnitude of vector C. 5. A car is driven (motorcycle is ridden) for 34 km south, then west for 15 km, and, finally, 9 km in a direction 26 o east of north. Find the magnitude of the car s total displacement. Hint 1/ Decompose the vectors into east-west and north-south components. Hint 2/ Add or subtract the components as necessary in order to obtain two vectors: one in north-south direction and one in east-west direction. Adding these two vectors together gives a resultant vector, then the three vectors form a right triangle. Use Pythagorean theorem to find the magnitude of the resultant displacement vector. 6. The velocity vector of a particle is equal to v= ( 11.2 m / s) iˆ (15.5 m/ s) ˆj. What is the magnitude of this vector in m/s? Hint 1/ The velocity vector is already decomposed into i and j components. Hint 2/ Adding the two components graphically will give a resultant vector. The three vectors then will form a right triangle to which Pythagorean theorem can be applied to find the magnitude of the resultant vector. V. Relative Motion 7
8 1. The speed of a bicyclist that is riding in the direction of the wind is 10 km/h relative to the wind. If the speed of the wind is 7 km/h relative to the ground, what is the speed of the bicyclist relative to the ground? The velocity of the bicyclist relative to the ground is equal to the velocity of the bicyclist relative to the wind plus the velocity of the wind relative to the ground: v BG = v BW + v WG. 2. John (Jacob, Dave, Bryan, Chris, Terry, Kevin, Joe, Mike) runs at 10 km/h relative to the ground. He throws a rock (stone, object) in the opposite direction with the speed of 10 km/h relative to him. What is the velocity of the rock relative to the ground? (Assume that John is moving in the positive direction of the x- axis). The velocity of the rock relative to the ground is equal to the velocity of the rock relative to the boy plus the velocity of the boy relative to the ground: v RG = v RB + v BG. Note that John throws the rock in the opposite direction he is running, so the velocity of the object relative to the boy is negative. 3. The speed of each of the two trains that are approaching each other is 90 km/h relative to the ground. What is the speed of one of the trains relative to the other? The velocity of the first train relative to the second train is equal to the velocity of the first train relative to the ground plus the velocity of the second train relative to the ground: v T1T2 = v T1G + v T2G. 4. A boat is traveling downstream at 20 km/h with respect to the water. If a person on the boat walks from front to rear at 3 km/h with respect to the boat and the speed of the water is 5 km/h relative to the ground, what is the velocity of the person on the boat relative to the ground? Assume that the water is moving in the positive direction of the x-axis. Step 1: First we will find the velocity of the person relative to the water. The velocity of the person relative to the water is equal to the velocity of the person relative to the boat plus the velocity of the boat relative to the water: v PW = v PB + v BW. You will use this velocity (v PW ) in Step 2. Note that the boat is moving downstream and the person walks from the front of the boat to the rear i.e. in the opposite direction. This means that the velocity of the person relative to the boat is negative. Step 2: Now we will find the velocity of the person relative to the ground. The velocity of the person relative to the ground is equal to the velocity of the person relative to the water (from Step 1) plus the velocity of the water relative to the ground: v PG = v PW + v WG. 5. You are swimming across the river at 4 km/h relative to the water. The speed of the water is 2 km/h relative to the ground. What should be the direction of your 8
9 velocity relative to the water in order for your velocity vector with respect to the ground to be perpendicular to the shore? (Give the measure of the angle that is adjacent to the line perpendicular to the shore. State your answer in deg). Hint 1/ The velocity of the person relative to the ground equals to the velocity of the person relative to the water plus the velocity of the water relative to the ground: v PG = v PW + v WG. The graphical vector addition forms a right triangle. Note that α is the angle we are asked to find. sin α = v WG / v PW, thus α = sin -1 (v WG / v PW ) 6. The boat is traveling upstream on a river. The speed of the water relative to the ground is 2 m/s. What is the speed of the boat relative to the water if its velocity relative to the ground is 16 m/s an angle of 10 o upstream? Hint 1/ The velocity of the boat relative to the ground equals to the velocity of the boat relative to the water plus the velocity of the water relative to the ground: v BG = v BW + v WG (see picture), where angle α = 10 o (according to the text of the problem). Hint 2/ We need to find the velocity of the boat relative to the water (v BW ). Thus, v BW = v BG v WG. Use trigonometric functions to break v BG into horizontal (x-) and vertical (y-) components, and then subtract respective components of the vectors v BG and v WG. (Note that v WG is directed in the opposite direction of the vertical component of v BG, so assuming that the vertical component of v BG is positive, the vertical component of vector v WG is negative). The horizontal component of vector v BG equals: (v BG ) x = v BG cos α. The vertical component of v BG equals: (v BG ) y = v BG sin α. The horizontal component of vector v WG equals: (v WG ) x = 0. The vertical component of v WG equals: (v WG ) y = - v WG. Thus, in unit vector form, vector v BW is represented as follows: v BW = (v BG cos α) i + (v BG sin α) j - (- v WG ) j = (v BG cos α) i + (v BG sin α + v WG ) j. Use Pythagorean theorem to find the magnitude of the vector v BW. 9
Physics 12. Chapter 1: Vector Analysis in Two Dimensions
Physics 12 Chapter 1: Vector Analysis in Two Dimensions 1. Definitions When studying mechanics in Physics 11, we have realized that there are two major types of quantities that we can measure for the systems
More informationKinematics in Two Dimensions; 2D- Vectors
Kinematics in Two Dimensions; 2D- Vectors Addition of Vectors Graphical Methods Below are two example vector additions of 1-D displacement vectors. For vectors in one dimension, simple addition and subtraction
More informationVector and Relative motion discussion/ in class notes. Projectile Motion discussion and launch angle problem. Finish 2 d motion and review for test
AP Physics 1 Unit 2: 2 Dimensional Kinematics Name: Date In Class Homework to completed that evening (before coming to next class period) 9/6 Tue (B) 9/7 Wed (C) 1D Kinematics Test Unit 2 Video 1: Vectors
More informationCHAPTER 3 KINEMATICS IN TWO DIMENSIONS; VECTORS
CHAPTER 3 KINEMATICS IN TWO DIMENSIONS; VECTORS OBJECTIVES After studying the material of this chapter, the student should be able to: represent the magnitude and direction of a vector using a protractor
More informationNewton 3 & Vectors. Action/Reaction. You Can OnlyTouch as Hard as You Are Touched 9/7/2009
Newton 3 & Vectors Action/Reaction When you lean against a wall, you exert a force on the wall. The wall simultaneously exerts an equal and opposite force on you. You Can OnlyTouch as Hard as You Are Touched
More informationNew concepts: scalars, vectors, unit vectors, vector components, vector equations, scalar product. reading assignment read chap 3
New concepts: scalars, vectors, unit vectors, vector components, vector equations, scalar product reading assignment read chap 3 Most physical quantities are described by a single number or variable examples:
More informationScalar Quantities - express only magnitude ie. time, distance, speed
Chapter 6 - Vectors Scalar Quantities - express only magnitude ie. time, distance, speed Vector Quantities - express magnitude and direction. ie. velocity 80 km/h, 58 displacement 10 km (E) acceleration
More information2-D Vector Equations have the same form as 1-D Kinematics. f i i
2-D Vector Equations have the same form as 1-D Kinematics v = v + at f i 1 r = r + v t+ at f i i 2 2 2-D Vector Equations have the same form as 1-D Kinematics v = viˆ+ v ˆj f x y = ( v + ati ) ˆ+ ( v +
More informationComponents of a Vector
Vectors (Ch. 1) A vector is a quantity that has a magnitude and a direction. Examples: velocity, displacement, force, acceleration, momentum Examples of scalars: speed, temperature, mass, length, time.
More informationTrigonometry Basics. Which side is opposite? It depends on the angle. θ 2. Y is opposite to θ 1 ; Y is adjacent to θ 2.
Trigonometry Basics Basic Terms θ (theta) variable for any angle. Hypotenuse longest side of a triangle. Opposite side opposite the angle (θ). Adjacent side next to the angle (θ). Which side is opposite?
More informationUnit 1, Lessons 2-5: Vectors in Two Dimensions
Unit 1, Lessons 2-5: Vectors in Two Dimensions Textbook Sign-Out Put your name in it and let s go! Check-In Any questions from last day s homework? Vector Addition 1. Find the resultant displacement
More informationDefinitions In physics we have two types of measurable quantities: vectors and scalars.
1 Definitions In physics we have two types of measurable quantities: vectors and scalars. Scalars: have magnitude (magnitude means size) only Examples of scalar quantities include time, mass, volume, area,
More informationKinematics in Two Dimensions; Vectors
Kinematics in Two Dimensions; Vectors Vectors & Scalars!! Scalars They are specified only by a number and units and have no direction associated with them, such as time, mass, and temperature.!! Vectors
More informationChapter 2 One-Dimensional Kinematics
Review: Chapter 2 One-Dimensional Kinematics Description of motion in one dimension Copyright 2010 Pearson Education, Inc. Review: Motion with Constant Acceleration Free fall: constant acceleration g =
More informationAP Physics 1 Summer Assignment 2018 Mrs. DeMaio
AP Physics 1 Summer Assignment 2018 Mrs. DeMaio demaiod@middletownk12.org Welcome to AP Physics 1 for the 2018-2019 school year. AP Physics 1 is an algebra based, introductory college-level physics course.
More informationChapter 3. Table of Contents. Section 1 Introduction to Vectors. Section 2 Vector Operations. Section 3 Projectile Motion. Section 4 Relative Motion
Two-Dimensional Motion and Vectors Table of Contents Section 1 Introduction to Vectors Section 2 Vector Operations Section 3 Projectile Motion Section 4 Relative Motion Section 1 Introduction to Vectors
More informationVectors. An Introduction
Vectors An Introduction There are two kinds of quantities Scalars are quantities that have magnitude only, such as position speed time mass Vectors are quantities that have both magnitude and direction,
More informationLecture PowerPoints. Chapter 3 Physics for Scientists & Engineers, with Modern Physics, 4 th edition Giancoli
Lecture PowerPoints Chapter 3 Physics for Scientists & Engineers, with Modern Physics, 4 th edition Giancoli 2009 Pearson Education, Inc. This work is protected by United States copyright laws and is provided
More informationCHAPTER 2: VECTOR COMPONENTS DESCRIBE MOTION IN TWO DIMENSIONS
CHAPTER 2: VECTOR COMPOETS DESCRIBE MOTIO I TWO DIMESIOS 2.1 Vector Methods in One Dimension Vectors may be pictured with sketches in which arrows represent quantities such as displacement, force and velocity.
More informationVector Quantities A quantity such as force, that has both magnitude and direction. Examples: Velocity, Acceleration
Projectile Motion Vector Quantities A quantity such as force, that has both magnitude and direction. Examples: Velocity, Acceleration Scalar Quantities A quantity such as mass, volume, and time, which
More informationAdding Vectors in Two Dimensions
Slide 37 / 125 Adding Vectors in Two Dimensions Return to Table of Contents Last year, we learned how to add vectors along a single axis. The example we used was for adding two displacements. Slide 38
More informationIntroduction to vectors
Lecture 4 Introduction to vectors Course website: http://facult.uml.edu/andri_danlov/teaching/phsicsi Lecture Capture: http://echo360.uml.edu/danlov2013/phsics1fall.html 95.141, Fall 2013, Lecture 3 Outline
More informationChapter 4. Two-Dimensional Motion
Chapter 4. Two-Dimensional Motion 09/1/003 I. Intuitive (Understanding) Review Problems. 1. If a car (object, body, truck) moves with positive velocity and negative acceleration, it means that its a) speed
More informationToday s Lecture: Kinematics in Two Dimensions (continued) A little bit of chapter 4: Forces and Newton s Laws of Motion (next time)
Today s Lecture: Kinematics in Two Dimensions (continued) Relative Velocity - 2 Dimensions A little bit of chapter 4: Forces and Newton s Laws of Motion (next time) 27 September 2009 1 Relative Velocity
More informationSolutions to Physics: Principles with Applications, 5/E, Giancoli Chapter 3 CHAPTER 3
Solutions to Phsics: Principles with Applications, 5/E, Giancoli Chapter 3 CHAPTE 3 1. We choose the west and south coordinate sstem shown. For the components of the resultant we have W W = D 1 + D cos
More informationName: Class: Date: Solution x 1 = units y 1 = 0. x 2 = d 2 cos = = tan 1 y
Assessment Chapter Test B Teacher Notes and Answers Two-Dimensional Motion and Vectors CHAPTER TEST B (ADVANCED) 1. b 2. d 3. d x 1 = 3.0 10 1 cm east y 1 = 25 cm north x 2 = 15 cm west x tot = x 1 + x
More informationAP* PHYSICS B DESCRIBING MOTION: KINEMATICS IN TWO DIMENSIONS &VECTORS
AP* PHYSICS B DESCRIBING MOTION: KINEMATICS IN TWO DIMENSIONS &VECTORS The moment of truth has arrived! To discuss objects that move in something other than a straight line we need vectors. VECTORS Vectors
More informationToday s Lecture: Kinematics in Two Dimensions (continued) A little bit of chapter 4: Forces and Newton s Laws of Motion (next time)
Today s Lecture: Kinematics in Two Dimensions (continued) Relative Velocity - 2 Dimensions A little bit of chapter 4: Forces and Newton s Laws of Motion (next time) 29 September 2009 1 Question the moving
More informationPhysics Test Review: Mechanics Session: Name:
Directions: For each statement or question, write in the answer box, the number of the word or expression that, of those given, best completes the statement or answers the question. 1. The diagram below
More informationVector Addition and Subtraction: Graphical Methods
Vector Addition and Subtraction: Graphical Methods Bởi: OpenStaxCollege Displacement can be determined graphically using a scale map, such as this one of the Hawaiian Islands. A journey from Hawai i to
More informationStudent Exploration: Vectors
Name: Date: Student Exploration: Vectors Vocabulary: component, dot product, magnitude, resultant, scalar, unit vector notation, vector Prior Knowledge Question (Do this BEFORE using the Gizmo.) An airplane
More informationChapter 2. Motion In One Dimension
I. Displacement, Position, and Distance Chapter 2. Motion In One Dimension 1. John (Mike, Fred, Joe, Tom, Derek, Dan, James) walks (jogs, runs, drives) 10 m north. After that he turns around and walks
More informationObjectives and Essential Questions
VECTORS Objectives and Essential Questions Objectives Distinguish between basic trigonometric functions (SOH CAH TOA) Distinguish between vector and scalar quantities Add vectors using graphical and analytical
More informationb) (6) How far down the road did the car travel during the acceleration?
General Physics I Quiz 2 - Ch. 2-1D Kinematics June 17, 2009 Name: For full credit, make your work clear to the grader. Show the formulas you use, all the essential steps, and results with correct units
More informationChapter 3 Vectors in Physics. Copyright 2010 Pearson Education, Inc.
Chapter 3 Vectors in Physics Units of Chapter 3 Scalars Versus Vectors The Components of a Vector Adding and Subtracting Vectors Unit Vectors Position, Displacement, Velocity, and Acceleration Vectors
More informationWhat is Relative Motion
RELATIVE MOTION What is Relative Motion Strictly speaking all motion is relative to something. Usually that something is a reference point that is assumed to be at rest (i.e. the earth). Motion can be
More informationVectors and Kinematics Notes 1 Review
Velocity is defined as the change in displacement with respect to time. Vectors and Kinematics Notes 1 Review Note that this formula is only valid for finding constant velocity or average velocity. Also,
More informationVectors in Physics. Topics to review:
Vectors in Physics Topics to review: Scalars Versus Vectors The Components of a Vector Adding and Subtracting Vectors Unit Vectors Position, Displacement, Velocity, and Acceleration Vectors Relative Motion
More informationChapter 2 Mechanical Equilibrium
Chapter 2 Mechanical Equilibrium I. Force (2.1) A. force is a push or pull 1. A force is needed to change an object s state of motion 2. State of motion may be one of two things a. At rest b. Moving uniformly
More informationLesson 2. Physics 168. Luis Anchordoqui
Lesson 2 Physics 168 Luis Anchordoqui Deriving Constant-Acceleration Kinematic Equations To obtain an equation for position as a function of time! look at special case of motion with constant velocity!
More informationA SCALAR is ANY quantity in physics that has MAGNITUDE, but NOT a direction associated with it. Magnitude A numerical value with units.
Vectors and Scalars A SCALAR is ANY quantity in physics that has MAGNITUDE, but NOT a direction associated with it. Magnitude A numerical value with units. Scalar Example Speed Distance Age Heat Number
More informationVectors. AP/Honors Physics Mr. Velazquez
Vectors AP/Honors Physics Mr. Velazquez The Basics Any quantity that refers to a magnitude and a direction is known as a vector quantity. Velocity, acceleration, force, momentum, displacement Other quantities
More informationPrinciples and Problems. Chapter 6: Motion in Two Dimensions
PHYSICS Principles and Problems Chapter 6: Motion in Two Dimensions CHAPTER 6 Motion in Two Dimensions BIG IDEA You can use vectors and Newton s laws to describe projectile motion and circular motion.
More informationSpring 2010 Physics 141 Practice Exam II Phy141_mt1b.pdf
1. (15 points) You are given two vectors: A has length 10. and an angle of 60. o (with respect to the +x axis). B has length 10. and an angle of 200. o (with respect to the +x axis). a) Calculate the components
More informationKinematics. Vector solutions. Vectors
Kinematics Study of motion Accelerated vs unaccelerated motion Translational vs Rotational motion Vector solutions required for problems of 2- directional motion Vector solutions Possible solution sets
More informationy(t) = y 0 t! 1 2 gt 2. With y(t final ) = 0, we can solve this for v 0 : v 0 A ĵ. With A! ĵ =!2 and A! = (2) 2 + (!
1. The angle between the vector! A = 3î! 2 ĵ! 5 ˆk and the positive y axis, in degrees, is closest to: A) 19 B) 71 C) 90 D) 109 E) 161 The dot product between the vector! A = 3î! 2 ĵ! 5 ˆk and the unit
More informationPhysics 1-2 Mr. Chumbley
Physics 1-2 Mr. Chumbley Physical quantities can be categorized into one of two types of quantities A scalar is a physical quantity that has magnitude, but no direction A vector is a physical quantity
More informationPhysics 12 Unit 1: Kinematics Notes. Name: What you will be able to do by the end of this unit:
Physics 12 Unit 1: Kinematics Notes. Name: What you will be able to do by the end of this unit: B1. Perform vector analysis in one or two dimensions identify scalars and vectors resolve a vector into two
More informationVector Pretest. Name: Class: Date: Multiple Choice Identify the choice that best completes the statement or answers the question.
Name: Class: Date: Vector Pretest Multiple Choice Identify the choice that best completes the statement or answers the question.. A word meaning size often used to describe scalar quantities is: a. magma.
More informationQ3.1. A. 100 m B. 200 m C. 600 m D m E. zero. 500 m. 400 m. 300 m Pearson Education, Inc.
Q3.1 P 400 m Q A bicyclist starts at point P and travels around a triangular path that takes her through points Q and R before returning to point P. What is the magnitude of her net displacement for the
More informationChapter 3 Kinematics in Two Dimensions; Vectors
Chapter 3 Kinematics in Two Dimensions; Vectors Vectors and Scalars Addition of Vectors Graphical Methods (One and Two- Dimension) Multiplication of a Vector by a Scalar Subtraction of Vectors Graphical
More informationLecture4- Projectile Motion Chapter 4
1 / 32 Lecture4- Projectile Motion Chapter 4 Instructor: Prof. Noronha-Hostler Course Administrator: Prof. Roy Montalvo PHY-123 ANALYTICAL PHYSICS IA Phys- 123 Sep. 28 th, 2018 2 / 32 Objectives Vector
More information1. Two forces act concurrently on an object on a horizontal, frictionless surface, as shown in the diagram below.
Name Vectors Practice 1. Two forces act concurrently on an object on a horizontal, frictionless surface, as shown in the diagram below. What additional force, when applied to the object, will establish
More informationChapter 3 Kinematics in Two Dimensions; Vectors
Chapter 3 Kinematics in Two Dimensions; Vectors Vectors and Scalars Units of Chapter 3 Addition of Vectors Graphical Methods Subtraction of Vectors, and Multiplication of a Vector by a Scalar Adding Vectors
More informationPSI AP Physics 1 Kinematics. Free Response Problems
PSI AP Physics 1 Kinematics Free Response Problems 1. A car whose speed is 20 m/s passes a stationary motorcycle which immediately gives chase with a constant acceleration of 2.4 m/s 2. a. How far will
More informationVersion PREVIEW Vectors & 2D Chap. 3 sizemore (13756) 1
Version PREVIEW Vectors & 2D Chap. 3 sizemore (13756) 1 This print-out should have 73 questions. Multiple-choice questions may continue on the next column or page find all choices before answering. Rectangular
More informationPhys101 First Major-111 Zero Version Monday, October 17, 2011 Page: 1
Monday, October 17, 011 Page: 1 Q1. 1 b The speed-time relation of a moving particle is given by: v = at +, where v is the speed, t t + c is the time and a, b, c are constants. The dimensional formulae
More informationPractice Test What two units of measurement are necessary for describing speed?
Practice Test 1 1. What two units of measurement are necessary for describing speed? 2. What kind of speed is registered by an automobile? 3. What is the average speed in kilometers per hour for a horse
More informationProgressive Science Initiative. Click to go to website:
Slide 1 / 246 New Jersey Center for Teaching and Learning Progressive Science Initiative This material is made freely available at www.njctl.org and is intended for the non-commercial use of students and
More informationPhysics Chapter 3 Notes. Section 3-1: Introduction to Vectors (pages 80-83)
Physics Chapter 3 Notes Section 3-1: Introduction to Vectors (pages 80-83) We can use vectors to indicate both the magnitude of a quantity, and the direction. Vectors are often used in 2- dimensional problems.
More informationVector components and motion
Vector components and motion Objectives Distinguish between vectors and scalars and give examples of each. Use vector diagrams to interpret the relationships among vector quantities such as force and acceleration.
More informationChapter 3 Homework Packet. Conceptual Questions
Chapter 3 Homework Packet Conceptual Questions 1) Which one of the following is an example of a vector quantity? A) mass B) area C) distance D) velocity A vector quantity has both magnitude and direction.
More informationRELATIVE MOTION ANALYSIS (Section 12.10)
RELATIVE MOTION ANALYSIS (Section 1.10) Today s Objectives: Students will be able to: a) Understand translating frames of reference. b) Use translating frames of reference to analyze relative motion. APPLICATIONS
More informationVECTORS REVIEW. ii. How large is the angle between lines A and B? b. What is angle C? 45 o. 30 o. c. What is angle θ? d. How large is θ?
VECTOS EVIEW Solve the following geometric problems. a. Line touches the circle at a single point. Line etends through the center of the circle. i. What is line in reference to the circle? ii. How large
More informationSection Distance and displacment
Chapter 11 Motion Section 11.1 Distance and displacment Choosing a Frame of Reference What is needed to describe motion completely? A frame of reference is a system of objects that are not moving with
More information1. (P2.1A) The picture below shows a ball rolling along a table at 1 second time intervals. What is the object s average velocity after 6 seconds?
PHYSICS FINAL EXAM REVIEW FIRST SEMESTER (01/2017) UNIT 1 Motion P2.1 A Calculate the average speed of an object using the change of position and elapsed time. P2.1B Represent the velocities for linear
More informationChapter 4 Kinematics II: Motion in Two and Three Dimensions
Chapter 4 Kinematics II: Motion in Two and Three Dimensions Demonstrations: 1) Ball falls down and another falls out 2) Parabolic and straight line motion from two different frames. The truck with a dropping
More informationVectors and 2D Kinematics. AIT AP Physics C
Vectors and 2D Kinematics Coordinate Systems Used to describe the position of a point in space Coordinate system consists of a fixed reference point called the origin specific axes with scales and labels
More informationVectors. Chapter 3. Arithmetic. Resultant. Drawing Vectors. Sometimes objects have two velocities! Sometimes direction matters!
Vectors Chapter 3 Vector and Vector Addition Sometimes direction matters! (vector) Force Velocity Momentum Sometimes it doesn t! (scalar) Mass Speed Time Arithmetic Arithmetic works for scalars. 2 apples
More informationVectors. Introduction. Prof Dr Ahmet ATAÇ
Chapter 3 Vectors Vectors Vector quantities Physical quantities that have both n u m e r i c a l a n d d i r e c t i o n a l properties Mathematical operations of vectors in this chapter A d d i t i o
More informationChapter 3. Kinematics in Two Dimensions
Chapter 3 Kinematics in Two Dimensions 3.1 Trigonometry 3.1 Trigonometry sin! = h o h cos! = h a h tan! = h o h a 3.1 Trigonometry tan! = h o h a tan50! = h o 67.2m h o = tan50! ( 67.2m) = 80.0m 3.1 Trigonometry!
More informationPreliminary Physics. Moving About. DUXCollege. Week 2. Student name:. Class code:.. Teacher name:.
Week 2 Student name:. Class code:.. Teacher name:. DUXCollege Week 2 Theory 1 Present information graphically of: o Displacement vs time o Velocity vs time for objects with uniform and non-uniform linear
More informationChapter 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
More informationUnit 1: Math Toolbox Math Review Guiding Light #1
Unit 1: Math Toolbox Math Review Guiding Light #1 Academic Physics Unit 1: Math Toolbox Math Review Guiding Light #1 Table of Contents Topic Slides Algebra Review 2 8 Trigonometry Review 9 16 Scalar &
More informationElectrical Theory. Mathematics Review. PJM State & Member Training Dept. PJM /22/2018
Electrical Theory Mathematics Review PJM State & Member Training Dept. PJM 2018 Objectives By the end of this presentation the Learner should be able to: Use the basics of trigonometry to calculate the
More informationThe Science of Physics
Assessment The Science of Physics Chapter Test B MULTIPLE CHOICE In the space provided, write the letter of the term or phrase that best completes each statement or best answers each question. 1. A hiker
More information1. Less than before. 2. Greater than before. 3. No change. correct
Version One Homework 3 Schemm 54321 Oct 22, 2004 1 This print-out should have 19 questions. Multiple-choice questions may continue on the next column or page find all choices before answering. The due
More informationTest 1 -Practice (Kinematics)
Name: ate: 1. car travels a distance of 98 meters in 10 seconds. What is the average speed of the car during this 10-second interval? 4.9 m/s 9.8 m/s 49 m/s 98 m/s 4. The diagram shown represents a force
More informationVectors A Guideline For Motion
AP Physics-1 Vectors A Guideline For Motion Introduction: You deal with scalar quantities in many aspects of your everyday activities. For example, you know that 2 liters plus 2 liters is 4 liters. The
More informationSB 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
More informationIn 1-D, all we needed was x. For 2-D motion, we'll need a displacement vector made up of two components: r = r x + r y + r z
D Kinematics 1. Introduction 1. Vectors. Independence of Motion 3. Independence of Motion 4. x-y motions. Projectile Motion 3. Relative motion Introduction Using + or signs was ok in 1 dimension but is
More informationKinematics Multiple- Choice Questions (answers on page 16)
Kinematics Multiple- Choice Questions (answers on page 16) 1. An object moves around a circular path of radius R. The object starts from point A, goes to point B and describes an arc of half of the circle.
More informationTOPIC 1.1: KINEMATICS
TOPIC.: KINEMATICS S4P-- S4P-- Derive the special equations for constant acceleration. Include: v= v+ a t; d = v t+ a t ; v = v + a d Solve problems for objects moving in a straight line with a constant
More informationFORCE TABLE INTRODUCTION
FORCE TABLE INTRODUCTION All measurable quantities can be classified as either a scalar 1 or a vector 2. A scalar has only magnitude while a vector has both magnitude and direction. Examples of scalar
More informationPHYSICS 221, FALL 2009 EXAM #1 SOLUTIONS WEDNESDAY, SEPTEMBER 30, 2009
PHYSICS 221, FALL 2009 EXAM #1 SOLUTIONS WEDNESDAY, SEPTEMBER 30, 2009 Note: The unit vectors in the +x, +y, and +z directions of a right-handed Cartesian coordinate system are î, ĵ, and ˆk, respectively.
More informationUNCORRECTED PAGE PROOFS
TOPIC 3 Motion in two dimensions 3.1 Overview 3.1.1 Module 1: Kinematics Motion on a Plane Inquiry question: How is the motion of an object that changes its direction of movement on a plane described?
More informationHomework due Nov 28 Physics
Homework due Nov 28 Physics Name Base your answers to questions 1 through 4 on the information and vector diagram below and on your knowledge of physics. A hiker starts at point P and walks 2.0 kilometers
More informationHalliday/Resnick/Walker 7e Chapter 3
HRW 7e Chapter 3 Page 1 of 7 Halliday/Resnick/Walker 7e Chapter 3 1. The x and the y components of a vector a lying on the xy plane are given by a = acos θ, a = asinθ x y where a = a is the magnitude and
More informationINTRODUCTION AND KINEMATICS. Physics Unit 1 Chapters 1-3
INTRODUCTION AND KINEMATICS Physics Unit 1 Chapters 1-3 This Slideshow was developed to accompany the textbook OpenStax Physics Available for free at https://openstaxcollege.org/textbooks/college-physics
More informationUnit 1 Representing and Operations with Vectors. Over the years you have come to accept various mathematical concepts or properties:
Lesson1.notebook November 27, 2012 Algebra Unit 1 Representing and Operations with Vectors Over the years you have come to accept various mathematical concepts or properties: Communative Property Associative
More informationPhysics 40 Chapter 3: Vectors
Physics 40 Chapter 3: Vectors Cartesian Coordinate System Also called rectangular coordinate system x-and y- axes intersect at the origin Points are labeled (x,y) Polar Coordinate System Origin and reference
More informationName: Total Points: Physics 201. Midterm 1
Physics 201 Midterm 1 QUESTION 1 [25 points] An object moves in 1 dimension It starts at rest and uniformly accelerates at 5m/s 2 for 2s It then moves with constant velocity for 4s It then uniformly accelerates
More informationPhys101-T121-First Major Exam Zero Version, choice A is the correct answer
Phys101-T121-First Major Exam Zero Version, choice A is the correct answer Q1. Find the mass of a solid cylinder of copper with a radius of 5.00 cm and a height of 10.0 inches if the density of copper
More informationMultiple-Choice Questions
Multiple-Choice Questions 1. A rock is thrown straight up from the edge of a cliff. The rock reaches the maximum height of 15 m above the edge and then falls down to the bottom of the cliff 35 m below
More informationUNIT V: Multi-Dimensional Kinematics and Dynamics Page 1
UNIT V: Multi-Dimensional Kinematics and Dynamics Page 1 UNIT V: Multi-Dimensional Kinematics and Dynamics As we have already discussed, the study of the rules of nature (a.k.a. Physics) involves both
More informationPhysics 3214 Unit 1 Motion. Vectors and Frames of Reference
Physics 3214 Unit 1 Motion Vectors and Frames of Reference Review Significant Digits 1D Vector Addition BUT First. Diagnostic QuizTime Rules for Significant DigitsRule #1 All non zero digits are ALWAYS
More informationIntroduction to Mechanics Motion in 2 Dimensions
Introduction to Mechanics Motion in 2 Dimensions Lana heridan De Anza College Oct 17, 2017 Last time vectors and trig Overview wrap up vectors introduction to motion in 2 dimensions constant velocity in
More informationFind graphically, using scaled diagram, following vectors (both magnitude and direction):
1 HOMEWORK 1 on VECTORS: use ruler and protractor, please!!! 1. v 1 = 3m/s, E and v = 4m/s, 3 Find graphically, using scaled diagram, following vectors (both magnitude and direction): a. v = v 1 + v b.
More informationAcceleration and Velocity PreTest (Chap 9)
Science 10 Name: Ver: A Date: Acceleration and Velocity PreTest (Chap 9) 1. Which of the following is a unit of acceleration? a. s 2 b. m 2 c. m/s d. m/s/s 2. Data is plotted on a graph with velocity on
More informationKinematics in Two-Dimensions
Slide 1 / 92 Slide 2 / 92 Kinematics in Two-Dimensions www.njctl.org Slide 3 / 92 How to Use this File Each topic is composed of brief direct instruction There are formative assessment questions after
More information