Correction key. Example of an appropriate method. be the wind vector x = 120 and x = y = 160 and y = 10.
|
|
- Alexandrina Wilcox
- 5 years ago
- Views:
Transcription
1 Correction key 1 D Example of an appropriate method /4 Let x, y be the wind vector (km) y 100, 150 x, y 10, x, 150 y 10, withot wind with wind x = 10 and x = y = 160 and y = 10 City A 100 x (km) Therefore x, y 0, 10 The speed of the wind: 0, Answer The wind speed is approximately.36 km/h.
2 3 Example of an appropriate method Draw the vector. Since the adjacent angles in a parallelogram are spplementary, w = 10 Therefore, sing the Cosine Law v 60 w 3v w cos 10 w 13 w Answer The magnitde of the vector is 3.6 nits.
3 4 Example of an appropriate method Measre of angle A m A = = 100 since two consective angle in a parallelogram are spplementary. A 100 F res 100 N 50 N Resltant force (strength) F res 100cos F res N Direction of resltant force sin sin 50 sin θ θ 4.38 The direction is , so abot
4 Answer Tim mst apply a force of N with a direction of A 6 D 7 D
5 8 Example of an acceptable soltion Given the resltant vector Magnitde of the resltant vector θ = cos d 44.7 Direction v 44.7 sin 45 8 sin θ sin = = = 6.7 Answer: The reslting speed of the hot air balloon is 44.7 km/h in a direction of 6.7.
6 9 Example of an appropriate method Components of vector AB AB = ( , 00 15) = (50, 75) Components of the nknown vector v? AB B? AB v? = (50, 75) (0, -15) A v AB?? = (50 0, )? = (30, 90) Direction of the nknown vector 90 tan = ? 90 km 30 km Answer: To the nearest degree, the pilot shold point the plane at an angle of 1 relative to the east in order to reach airport B. Note: Do not penalize stdents who did not rond off their final answer or who made a mistake in ronding if off.
7 Stdents who sed an appropriate method in order to determine the components of the nknown vector have shown that they have a partial nderstanding of the problem. 10 B 11 c = cm Accept any answer between 45.9 cm and 46 cm. 1 C 13 Ronded to the nearest tenth v is A 15 B
8
9 16 Example of an acceptable soltion N W B a = 50 E C c = 00 b =? A AB c 00 km/h, North BC a 50 km/h, from Northwest AC b? In ABC b = a + c ac cos (B) b = cos (45) b = = km Also
10 A sin B sin C sin a b c sin A sin sin 45-1 sin A A sin A A as shown or N E Answer: The reslting speed of the airplane is km/h in a direction of 1.1 or N 1.1 E.
11 17 Example of an appropriate soltion Angle between vectors θ v v cos θ 54 1 v 54 1 v 54 6 v cos 60 1 v 9 cm 10 9 cm x y x cos 10 9 x 9 cos 10 x 8.86 y sin 10 9 y 9 sin 10 y 1.56 Answer: The horizontal, x, component is 8.9. The vertical, y, component is 1.6. Do not penalize stdents who did not rond, or ronded incorrectly.
12 18 To the nearest nit, the magnitde is 8 nits. To the nearest degree, the direction is W76N or eqivalent.
13 Vectors 1 Qadrilateral RSTU is a parallelogram and M is the point of intersection of its diagonals. Antoine lists the following vector operation statements: R S M U T 1) ) 3) 4) 5) ST SR MU UT UR SM RS RU RT MT MR MS MU 0 SR ST RT Which of these statements are tre A) 1, and 3 only C), 4 and 5 only B) 1, and 5 only D) 1, 3 and 4 only A plane goes from city A to city B. In a Cartesian plane, city A is at the origin and city B has coordinates (100, 150). If there is no wind, the flight lasts one hor. Unfortnately, there is a wind. If the pilot does not adjst his flight path, he will be at point (10, 160) after an hor. What is the speed of the wind? 3 Two nit vectors, and v, form a 60 angle as shown. v What is the magnitde of the vector w if w 3v? 60
14 4 Peter and Marie are plling on an object. The forces they applied are 100 N and 50 N respectively bt in different directions: 40 and 10. The sitation is represented below. 100 N 50 N Tim is going to replace them. What force mst Tim apply to prodce the same effect on the object (strength and direction)? 5 Given the following prism having a rectanglar base. E F A B H G D C Which vector is eqivalent to the resltant of the expression AD + HE + AE? A) DH C) FB B) BE D) BC
15 6 The Egyptians sed an ingenios plley system to move the blocks of stone sed in the constrction of pyramids. To minimize the work needed to displace the blocks, they applied a force oriented at 6. (Work (Nm) is the scalar prodct of the force vector and the displacement vector.) 1500 N 6 00 m Ronded to the nearest Nm, what work is needed to displace a block of stone horizontally for a distance of 00 m, if the force applied to it is 1500 N oriented at 6 o? A) Nm C) Nm B) Nm D) Nm 7 Given the three vectors, v, and w. v = (-, -3) and w are represented in the Cartesian plane below: y w x Which of the following statements is TRUE? A) v and - are opposite. B) and v are eqivalent. C) w and ( v + w ) are perpendiclar. D) and 3 v are collinear.
16 8 A hot air balloon is flying de soth at 50 km/h. N Sddenly, the wind starts blowing from the sotheast at 8 km/h. N-W N-E What is the reslting speed and direction of the hot air balloon? W S-W S-E E S 9 An airplane leaves airport A and mst fly to airport B. In the Cartesian plane on the right, these airports are represented by points A and B respectively. The scale of the graph is in kilometres. y O N S E Dring the flight, the plane enconters a steady wind. This wind is represented by the vector v = (0, -15). A (150, 15) B (400, 00) x The pilot steers the plane so as to negate the effect of the wind. To the nearest degree, at what angle relative to the east shold the pilot point the plane in order to reach airport B? 10 Given vectors = (-3, 9), v = (6, ), w = (6, -18) and k 0. Which of the following statements is FALSE? A) k kv k v B) k v k w = k v w C) and w are collinear. D) and v are orthogonal.
17 11 Consider the two vectors and v. The magnitde of is 10 cm at an angle of 140. The magnitde of v is 15 cm at an angle of 40. c 3v What is the magnitde of c? 1 The magnitdes of two vectors are 1 and 16 respectively, and their directions differ by 60 degrees. What is the magnitde of the resltant of these two vectors? A) -96 C) 4.34 B) 14.4 D) Given vectors and v where: = AB with A(-5, 7) and B(3, -5) v = (6, 3) Find + v. Rond yor answer to the nearest tenth.
18 14 An airplane flying East at 150 km/h enconters a 50 km/h wind blowing in a 30 East of North direction. What will be the airplane's resltant velocity? A) 180 km/h [E 14 N] C) 00 km/h [N 30 E] B) 195 km/h [E 7 N] D) 13 km/h [E 19 S] 15 Given vectors and v shown below. v Which of the following vectors represents the resltant, r, of v? A) r C) r B) r D) r 16 An airplane is flying de north at 00 km/h. N Sddenly, the wind starts blowing from the northwest at 50 km/h. W N-W N-E E What is the reslting speed and direction of the airplane? S-W S S-E
19 17 Given v = 54. The magnitde of is 1 cm and its direction is 70. The direction of v is 10. y v x What are the components of v, to the nearest tenth? 18 On a compter screen, an alien ship was travelling at a very rapid speed. When it reached point A(3, -), it sddenly exploded with one piece moving to point B(-1, 3) and the other to point C(5, 1). N B(-1, 3) W E v C(5, 1) S A(3, -) What is the sm of vectors and v? Give the magnitde of the resltant vector to the nearest nit, and its direction to the nearest degree.
Which of these statements are true? A) 1, 2 and 3 only C) 2, 4 and 5 only. B) 1, 2 and 5 only D) 1, 3 and 4 only
Name : 1 Qadrilateral RSTU is a parallelogram and M is the point of intersection of its diagonals. S M T ntoine lists the following vector operation statements: R U 1) ST + SR MU ) UT + UR SM 3) RS + RU
More informationMathematics 5 SN Guide
Mathematics 5 SN Guide 1 Quadrilateral RSTU is a parallelogram and M is the point of intersection of its diagonals. S M T Antoine lists the following vector operation statements: R U 1) ST SR 2MU 2) UT
More informationCONTENTS. INTRODUCTION MEQ curriculum objectives for vectors (8% of year). page 2 What is a vector? What is a scalar? page 3, 4
CONTENTS INTRODUCTION MEQ crriclm objectives for vectors (8% of year). page 2 What is a vector? What is a scalar? page 3, 4 VECTOR CONCEPTS FROM GEOMETRIC AND ALGEBRAIC PERSPECTIVES page 1 Representation
More informationLesson 81: The Cross Product of Vectors
Lesson 8: The Cross Prodct of Vectors IBHL - SANTOWSKI In this lesson yo will learn how to find the cross prodct of two ectors how to find an orthogonal ector to a plane defined by two ectors how to find
More informationsin u 5 opp } cos u 5 adj } hyp opposite csc u 5 hyp } sec u 5 hyp } opp Using Inverse Trigonometric Functions
13 Big Idea 1 CHAPTER SUMMARY BIG IDEAS Using Trigonometric Fnctions Algebra classzone.com Electronic Fnction Library For Yor Notebook hypotense acent osite sine cosine tangent sin 5 hyp cos 5 hyp tan
More informationVectors. Vectors ( 向量 ) Representation of Vectors. Special Vectors. Equal vectors. Chapter 16
Vectors ( 向量 ) Chapter 16 2D Vectors A vector is a line which has both magnitde and direction. For example, in a weather report yo may hear a statement like the wind is blowing at 25 knots ( 海浬 ) in the
More informationVectors in Rn un. This definition of norm is an extension of the Pythagorean Theorem. Consider the vector u = (5, 8) in R 2
MATH 307 Vectors in Rn Dr. Neal, WKU Matrices of dimension 1 n can be thoght of as coordinates, or ectors, in n- dimensional space R n. We can perform special calclations on these ectors. In particlar,
More informationThe Cross Product of Two Vectors in Space DEFINITION. Cross Product. u * v = s ƒ u ƒƒv ƒ sin ud n
12.4 The Cross Prodct 873 12.4 The Cross Prodct In stdying lines in the plane, when we needed to describe how a line was tilting, we sed the notions of slope and angle of inclination. In space, we want
More informationMotion in One Dimension. A body is moving with velocity 3ms towards East. After s its velocity becomes 4ms towards North. The average acceleration of the body is a) 7ms b) 7ms c) 5ms d) ms. A boy standing
More informationDirectio n I. Model Problems. In the following problem you will learn to show vector addition using the tail-to-tip method. Find.
Vectors represent magnitde and direction. Vectors can be named like a ray, or in bold with one letter in bold, (or in handwritten text). The magnitde of ector is the size of a ector often representing
More informationDATE: MATH ANALYSIS 2 CHAPTER 12: VECTORS & DETERMINANTS
NAME: PERIOD: DATE: MATH ANALYSIS 2 MR. MELLINA CHAPTER 12: VECTORS & DETERMINANTS Sections: v 12.1 Geometric Representation of Vectors v 12.2 Algebraic Representation of Vectors v 12.3 Vector and Parametric
More informationC) ) 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
More informationEinstein Classes, Unit No. 102, 103, Vardhman Ring Road Plaza, Vikas Puri Extn., Outer Ring Road New Delhi , Ph. : ,
PK K I N E M A T I C S Syllabs : Frame of reference. Motion in a straight line : Position-time graph, speed and velocity. Uniform and non-niform motion, average speed and instantaneos velocity. Uniformly
More information8-2 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.
More informationLecture 3. (2) Last time: 3D space. The dot product. Dan Nichols January 30, 2018
Lectre 3 The dot prodct Dan Nichols nichols@math.mass.ed MATH 33, Spring 018 Uniersity of Massachsetts Janary 30, 018 () Last time: 3D space Right-hand rle, the three coordinate planes 3D coordinate system:
More informationPhysics 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 informationu v u v v 2 v u 5, 12, v 3, 2 3. u v u 3i 4j, v 7i 2j u v u 4i 2j, v i j 6. u v u v u i 2j, v 2i j 9.
Section. Vectors and Dot Prodcts 53 Vocablary Check 1. dot prodct. 3. orthogonal. \ 5. proj PQ F PQ \ ; F PQ \ 1., 1,, 3. 5, 1, 3, 3., 1,, 3 13 9 53 1 9 13 11., 5, 1, 5. i j, i j. 3i j, 7i j 1 5 1 1 37
More information6.4 VECTORS AND DOT PRODUCTS
458 Chapter 6 Additional Topics in Trigonometry 6.4 VECTORS AND DOT PRODUCTS What yo shold learn ind the dot prodct of two ectors and se the properties of the dot prodct. ind the angle between two ectors
More information2 and v! = 3 i! + 5 j! are given.
1. ABCD is a rectangle and O is the midpoint of [AB]. D C 2. The vectors i!, j! are unit vectors along the x-axis and y-axis respectively. The vectors u! = i! + j! 2 and v! = 3 i! + 5 j! are given. (a)
More informationBC 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
More informationm = Average Rate of Change (Secant Slope) Example:
Average Rate o Change Secant Slope Deinition: The average change secant slope o a nction over a particlar interval [a, b] or [a, ]. Eample: What is the average rate o change o the nction over the interval
More informationPhysicsAndMathsTutor.com
. Two smooth niform spheres S and T have eqal radii. The mass of S is 0. kg and the mass of T is 0.6 kg. The spheres are moving on a smooth horizontal plane and collide obliqely. Immediately before the
More informationSECTION 6.7. The Dot Product. Preview Exercises. 754 Chapter 6 Additional Topics in Trigonometry. 7 w u 7 2 =?. 7 v 77w7
754 Chapter 6 Additional Topics in Trigonometry 115. Yo ant to fly yor small plane de north, bt there is a 75-kilometer ind bloing from est to east. a. Find the direction angle for here yo shold head the
More informationSkills Practice Skills Practice for Lesson 14.1
Skills Practice Skills Practice for Lesson 1.1 Name Date By Air and By Sea Introduction to Vectors Vocabulary Match each term to its corresponding definition. 1. column vector notation a. a quantity that
More informationMath 144 Activity #10 Applications of Vectors
144 p 1 Math 144 Actiity #10 Applications of Vectors In the last actiity, yo were introdced to ectors. In this actiity yo will look at some of the applications of ectors. Let the position ector = a, b
More informationFind a vector equation for the line through R parallel to the line (PQ) (Total 6 marks)
1. The points P( 2, 4), Q (3, 1) and R (1, 6) are shown in the diagram below. (a) Find the vector PQ. (b) Find a vector equation for the line through R parallel to the line (PQ). 2. The position vector
More informationLecture Notes: Finite Element Analysis, J.E. Akin, Rice University
9. TRUSS ANALYSIS... 1 9.1 PLANAR TRUSS... 1 9. SPACE TRUSS... 11 9.3 SUMMARY... 1 9.4 EXERCISES... 15 9. Trss analysis 9.1 Planar trss: The differential eqation for the eqilibrim of an elastic bar (above)
More informationBELLWORK 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
More informationSUPPLEMENT I. Example. Graph the vector 4, 3. Definition. Given two points A(x 1, y 1 ) and B(x 2, y 2 ), the vector represented by # AB is # AB =,
SUPPLEMENT I 1. Vectors Definition. A vector is a quantity that has both a magnitude and a direction. A twodimensional vector is an ordered pair a = a 1, a 2 of real numbers. The numbers a 1 and a 2 are
More informationCongruence 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
More informationI. Model Problems. II. Vector Basics III. Addition Of Vectors IV. Find Resultant Magnitude V. Find Angle associated with Resultant VI.
www.mathworksheetsgo.com On Twitter: twitter.com/mathprintables I. Model Problems. II. Vector Basics III. Addition Of Vectors IV. Find Resltant Magnitde V. Find Angle associated with Resltant VI. Answer
More information5. A triangle has sides represented by the vectors (1, 2) and (5, 6). Determine the vector representing the third side.
Vectors EXAM review Problem 1 = 8 and = 1 a) Find the net force, assume that points North, and points East b) Find the equilibrant force 2 = 15, = 7, and the angle between and is 60 What is the magnitude
More informationRight Trapezoid Cover for Triangles of Perimeter Two
Kasetsart J (Nat Sci) 45 : 75-7 (0) Right Trapezoid Cover for Triangles of Perimeter Two Banyat Sroysang ABSTRACT A convex region covers a family of arcs if it contains a congrent copy of every arc in
More informationApplications of Trigonometry and Vectors. Copyright 2017, 2013, 2009 Pearson Education, Inc.
7 Applications of Trigonometry and Vectors Copyright 2017, 2013, 2009 Pearson Education, Inc. 1 7.4 Geometrically Defined Vectors and Applications Basic Terminology The Equilibrant Incline Applications
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 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 informationb g 6. P 2 4 π b g b g of the way from A to B. LATE AND ABSENT HOMEWORK IS ACCEPTED UP TO THE TIME OF THE CHAPTER TEST ON ASSIGNMENT DUE
A Trig/Math Anal Name No LATE AND ABSENT HOMEWORK IS ACCEPTED UP TO THE TIME OF THE CHAPTER TEST ON HW NO. SECTIONS (Brown Book) ASSIGNMENT DUE V 1 1 1/1 Practice Set A V 1 3 Practice Set B #1 1 V B 1
More informationSolutions to 1 st Major 111
Solutions to 1 st Major 111 Q1. Consider a cube of iron of mass 8.0 kg and side 4.0 inches. What is its density in kg/m 3? (1 inch = 2.54 cm) A) 7.6 10 3 B) 6.9 10 3 C) 9.8 10 3 D) 4.3 10 3 2.54 cm 1 m
More informationVectors. chapter. Figure 3.1 Designation of points in a Cartesian coordinate system. Every point is labeled with coordinates (x, y).
chapter 3 Vectors 3.1 Coordinate stems 3.2 Vector and calar Qantities 3.3 ome Properties of Vectors 3.4 Components of a Vector and Unit Vectors In or std of phsics, we often need to work with phsical qantities
More informationMomentum Equation. Necessary because body is not made up of a fixed assembly of particles Its volume is the same however Imaginary
Momentm Eqation Interest in the momentm eqation: Qantification of proplsion rates esign strctres for power generation esign of pipeline systems to withstand forces at bends and other places where the flow
More informationMt. Douglas Secondary
Foundations of Math 11 Section 3.4 pplied Problems 151 3.4 pplied Problems The Law of Sines and the Law of Cosines are particularly useful for solving applied problems. Please remember when using the Law
More informationA 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
More information9.1 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
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 informationStandardized Test Practice - Cumulative, Chapters What is the value of x in the figure below?
1. What is the value of x in the figure below? 2. A baseball diamond is a square with 90-ft sides. What is the length from 3rd base to 1st base? Round to the nearest tenth. A 22.5 B 23 C 23.5 D 24 Use
More information1 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
More informationSpeed ( v ) is the distance an object travels during a given time interval divided by the time interval.
v 8.2 Average Velocity Speed ( v ) is the distance an object travels during a given time interval divided by the time interval. Speed is a scalar quantity. The SI unit for speed is metres per second (m/s).
More information4.4 Moment of a Force About a Line
4.4 Moment of a orce bot a Line 4.4 Moment of a orce bot a Line Eample 1, page 1 of 3 1. orce is applied to the end of gearshift lever DE. Determine the moment of abot shaft. State which wa the lever will
More information1.1 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,
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 informationII. Vector Basics 1. What is the magnitude and direction of """""#?! B What is the magnitude and direction of $% """""#? R
II. Vector Basics 1. What is the magnitde and direction of """""#?! B 8.5 A 3. What is the magnitde and direction of &' """"#? J 12 lb 28 70 K 2. What is the magnitde and direction of $% """""#? R T 4.5
More informationObliqe Projection. A body is projected from a point with different angles of projections 0 0, 35 0, 45 0, 60 0 with the horizontal bt with same initial speed. Their respective horizontal ranges are R,
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 informationb) The trend is for the average slope at x = 1 to decrease. The slope at x = 1 is 1.
Chapters 1 to 8 Course Review Chapters 1 to 8 Course Review Question 1 Page 509 a) i) ii) [2(16) 12 + 4][2 3+ 4] 4 1 [2(2.25) 4.5+ 4][2 3+ 4] 1.51 = 21 3 = 7 = 1 0.5 = 2 [2(1.21) 3.3+ 4][2 3+ 4] iii) =
More informationFOM 11 CHAPTER 3 TEST
Instructions: Show all required work! NO WORK = NO MARKS!!!!!! 1. Sketch a triangle that corresponds to the equation. (1 mark) Then, determine the third angle measure. (1 mark) Sketch: Measure of third
More informationPre-Calculus Vectors
Slide 1 / 159 Slide 2 / 159 Pre-Calculus Vectors 2015-03-24 www.njctl.org Slide 3 / 159 Table of Contents Intro to Vectors Converting Rectangular and Polar Forms Operations with Vectors Scalar Multiples
More informationElements of Coordinate System Transformations
B Elements of Coordinate System Transformations Coordinate system transformation is a powerfl tool for solving many geometrical and kinematic problems that pertain to the design of gear ctting tools and
More informationChapter 3. Vectors. θ that the vector forms with i ˆ is 15. I. Vectors and Scalars
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
More informationThe line that passes through the point A ( and parallel to the vector v = (a, b, c) has parametric equations:,,
Vectors: Lines in Space A straight line can be determined by any two points in space. A line can also be determined by specifying a point on it and a direction. The direction would be a non-zero parallel
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 informationDepartment of Physics, Korea University
Name: Department: Notice +2 ( 1) points per correct (incorrect) answer. No penalty for an unanswered question. Fill the blank ( ) with (8) if the statement is correct (incorrect).!!!: corrections to an
More informationPrerequisite Skills. y x =
Prerequisite Skills BLM 1 1... Solve Equations 1. Solve. 2x + 5 = 11 x 5 + 6 = 7 x 2 = 225 d) x 2 = 24 2 + 32 2 e) 60 2 + x 2 = 61 2 f) 13 2 12 2 = x 2 The Pythagorean Theorem 2. Find the measure of the
More informationVectors 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.
More informationAP Physics C Mechanics Vectors
1 AP Physics C Mechanics Vectors 2015 12 03 www.njctl.org 2 Scalar Versus Vector A scalar has only a physical quantity such as mass, speed, and time. A vector has both a magnitude and a direction associated
More informationVector 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
More informationSL Vector Practice The points P( 2, 4), Q (3, 1) and R (1, 6) are shown in the diagram below.
IB Math Standard Level Vector Practice 0506 SL Vector Practice 0506. The points P(, ), Q (, ) and R (, 6) are shown in the diagram below. Alei - Desert Academy (a) Find the vector PQ. (b) Find a vector
More information2015 Canadian Team Mathematics Contest
The CENTRE for EDUCATION in MATHEMATICS and COMPUTING cemc.uwaterloo.ca 205 Canadian Team Mathematics Contest April 205 Solutions 205 University of Waterloo 205 CTMC Solutions Page 2 Individual Problems.
More informationEXERCISES WAVE EQUATION. In Problems 1 and 2 solve the heat equation (1) subject to the given conditions. Assume a rod of length L.
.4 WAVE EQUATION 445 EXERCISES.3 In Problems and solve the heat eqation () sbject to the given conditions. Assme a rod of length.. (, t), (, t) (, ),, > >. (, t), (, t) (, ) ( ) 3. Find the temperatre
More informationVectors. February 1, 2010
Vectors Febrary 1, 2010 Motivation Location of projector from crrent position and orientation: direction of projector distance to projector (direction, distance=magnitde) vector Examples: Force Velocity
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 informationGround Rules. PC1221 Fundamentals of Physics I. Position and Displacement. Average Velocity. Lectures 7 and 8 Motion in Two Dimensions
PC11 Fndamentals of Physics I Lectres 7 and 8 Motion in Two Dimensions A/Prof Tay Sen Chan 1 Grond Rles Switch off yor handphone and paer Switch off yor laptop compter and keep it No talkin while lectre
More information2. Find the coordinates of the point where the line tangent to the parabola 2
00. lim 3 3 3 = (B) (C) 0 (D) (E). Find the coordinates of the point where the line tangent to the parabola y = 4 at = 4 intersects the ais of symmetry of the parabola. 3. If f () = 7 and f () = 3, then
More informationMath 302 Test 1 Review
Math Test Review. Given two points in R, x, y, z and x, y, z, show the point x + x, y + y, z + z is on the line between these two points and is the same distance from each of them. The line is rt x, y,
More informationMATH 151 Engineering Mathematics I
MATH 151 Engineering Mathematics I Spring 2018, WEEK 1 JoungDong Kim Week 1 Vectors, The Dot Product, Vector Functions and Parametric Curves. Section 1.1 Vectors Definition. A Vector is a quantity that
More informationCHAPTER 10 VECTORS POINTS TO REMEMBER
For more important questions visit : www4onocom CHAPTER 10 VECTORS POINTS TO REMEMBER A quantity that has magnitude as well as direction is called a vector It is denoted by a directed line segment Two
More informationSetting The K Value And Polarization Mode Of The Delta Undulator
LCLS-TN-4- Setting The Vale And Polarization Mode Of The Delta Undlator Zachary Wolf, Heinz-Dieter Nhn SLAC September 4, 04 Abstract This note provides the details for setting the longitdinal positions
More informationVIII - 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
More informationExponent Laws. a m a n = a m + n a m a n = a m n, a 0. ( ab) m = a m b m. ˆ m. = a m. a n = 1 a n, a 0. n n = a. Radicals. m a. n b Ë. m a. = mn.
Name:. Math 0- Formula Sheet Sequences and Series t n = t + ( n )d S n = n È t ÎÍ + ( n )d S n = n Ê Á t + t n ˆ t n = t r n Ê t r n ˆ Á S n =, r r S n = rt n t r, r S = t r, r Trigonometry Exponent Laws
More informationOpenStax-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
More informationPhysics ( (Chapter 4) (Motion in a Plane)
() Question 4.1: State, for each of the following physical quantities, if it is a scalar or a vector: Volume, mass, speed, acceleration, density, number of moles, velocity, angular frequency, displacement,
More informationDepartment of Industrial Engineering Statistical Quality Control presented by Dr. Eng. Abed Schokry
Department of Indstrial Engineering Statistical Qality Control presented by Dr. Eng. Abed Schokry Department of Indstrial Engineering Statistical Qality Control C and U Chart presented by Dr. Eng. Abed
More informationUnit 3 Practice Test Questions Trigonometry
Unit 3 Practice Test Questions Trigonometry Multiple Choice Identify the choice that best completes the statement or answers the question. 1. How you would determine the indicated angle measure, if it
More informationIntroduction to Vectors Pg. 279 # 1 6, 8, 9, 10 OR WS 1.1 Sept. 7. Vector Addition Pg. 290 # 3, 4, 6, 7, OR WS 1.2 Sept. 8
UNIT 1 INTRODUCTION TO VECTORS Lesson TOPIC Suggested Work Sept. 5 1.0 Review of Pre-requisite Skills Pg. 273 # 1 9 OR WS 1.0 Fill in Info sheet and get permission sheet signed. Bring in $3 for lesson
More information9.4 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
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 informationChapter 6 REVIEW. 6.1 Introduction to Vectors. 6.3 Multiplying a Vector by a Scalar. 6.2 Addition and Subtraction of Vectors
Chapter 6 REVIEW 6.1 Introduction to Vectors 1. For which of the following situations would a vector be a suitable mathematical model? Provide a reason for your decision. a) A car is travelling at 70 km/h
More informationu + 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
More information2012 GCSE Maths Tutor All Rights Reserved
2012 GCSE Maths Tutor All Rights Reserved www.gcsemathstutor.com This book is under copyright to GCSE Maths Tutor. However, it may be distributed freely provided it is not sold for profit. Contents angles
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 informationVECTORS. 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
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 informationVectors 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
More informationMECHANICS OF SOLIDS COMPRESSION MEMBERS TUTORIAL 2 INTERMEDIATE AND SHORT COMPRESSION MEMBERS
MECHANICS O SOIDS COMPRESSION MEMBERS TUTORIA INTERMEDIATE AND SHORT COMPRESSION MEMBERS Yo shold jdge yor progress by completing the self assessment exercises. On completion of this ttorial yo shold be
More informationStarting with the base and moving counterclockwise, the measured side lengths are 5.5 cm, 2.4 cm, 2.9 cm, 2.5 cm, 1.3 cm, and 2.7 cm.
Chapter 6 Geometric Vectors Chapter 6 Prerequisite Skills Chapter 6 Prerequisite Skills Question 1 Page 302 Starting with the base and moving counterclockwise, the measured side lengths are 5.5 cm, 2.4
More informationPhysics. Chapter 5 Newton s Third Law
Physics Chapter 5 Newton s Third Law Forces and Interactions In previous lessons, we defined a force as a push or pull. But in reality, no push or pull EVER occurs alone. They come in pairs. Some examples:
More informationFind the length of an arc that subtends a central angle of 45 in a circle of radius 8 m. Round your answer to 3 decimal places.
Chapter 6 Practice Test Find the radian measure of the angle with the given degree measure. (Round your answer to three decimal places.) 80 Find the degree measure of the angle with the given radian measure:
More informationConceptual Questions. Problems. 852 CHAPTER 29 Magnetic Fields
852 CHAPTER 29 Magnetic Fields magnitde crrent, and the niform magnetic field points in the positive direction. Rank the loops by the magnitde of the torqe eerted on them by the field from largest to smallest.
More informationVectors (Trigonometry Explanation)
Vectors (Trigonometry Explanation) CK12 Editor Say Thanks to the Authors Click http://www.ck12.org/saythanks (No sign in required) To access a customizable version of this book, as well as other interactive
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 informationVectors 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
More information