Prep for Engineering Studies PHYS-100
|
|
- Heather Page
- 5 years ago
- Views:
Transcription
1 Prep for Engineering Studies PHYS-100 Winter Dr. Joseph Trout
2 Pythagoras was a Greek philosopher who made important developments in mathematics, astronomy, and the theory of music. The theorem now known as Pythagoras's theorem was known to the Babylonians 1000 years earlier but he may have been the first to prove it. 2
3 r 2 =x 2 y 2 y x 3
4 r= x 2 y 2 y x 4
5 r= 4 m 2 3m 2 = 16 m 2 9m 2 = 25m 2 =5m r y=3 m x=4 m 5
6 r= 6 m 2 7m 2 = 36 m 2 49m 2 = 8 2 =9.22m r y=7m x=6 m 6
7 r y sin = y r cos = x r x tan = y x r= x 2 y 2 7
8 r=5 y=4 sin = y r =4 5 cos = x r =3 5 x=3 tan = y x =4 3 r= x 2 y 2 r= =5 8
9 hyp opp sin = opp hyp cos = adj hyp adj tan = opp adj 9
10 hyp opp sin = opp hyp cos = adj hyp adj tan = opp adj 10
11 y x 11
12 y 90 o 180 o 0 o 360 o x 270 o 12
13 r s=r = s r [ ]=radians 13
14 y 90 o 180 o 0 o 0 rad 360 o 2 rad x Whole Circle 270 o = s r =2 r r =2 radians 14
15 y 90 o 2 rad 180 o rad 0 o 0 rad x 360 o 2 rad Whole Circle 270 o 3 2 rad = s r =2 r r =2 radians 15
16 Scalar Magnitude only. Example: mass, distance, speed Example: m, x, v Vector Magnitude and Direction. Example: displacement,velocity, acceleration, force Example: x, v, a, F
17 Distance scalar magnitude of the total distance traveled. Displacement vector distance between final position and initial position AND the direction.
18 Displacement in One Dimension: Direction will either be positive or negative.
19 Distance vs. Displacement: distance= x=4.0 m X= -4.0 m X=-2.0 m X= 0.0 m X= 2.0 m X=4.0 m
20 Distance vs. Displacement: distance= x=4.0 m displacement= x=x f x i =4.0 m 0.0 m= 4.0 m X= -4.0 m X=-2.0 m X= 0.0 m X= 2.0 m X=4.0 m
21 Distance vs. Displacement: distance=4.0 m 8.0 m=12m X= -4.0 m X=-2.0 m X= 0.0 m X= 2.0 m X=4.0 m displacement x=x f x i = 4m 0m= 4m
22 Marathon distance = 26 miles Marathon displacement = -0.2iles Start Finish +x
23 Displacement = x= x f x i
24 Scalar Magnitude ONLY distance=iles mass=6 kg Vector Magnitude and Direction Example :Velocity v=40m/s North v=40m/s in positive x direction. 30 o v=3m/ s i 7 m/ s j 6 m/s k 24
25 y o =60 o x 25
26 j Vector Notation y axis z axis x axis i k 26
27 j Vector Notation B=3 m j i A=4 m i 27
28 j Vector Notation R= A B B=3 m j i A=4 m i 28
29 j Vector Notation R= A B R=4m i 3m j B=3 m j i A=4 m i 29
30 Pythagoras was a Greek philosopher who made important developments in mathematics, astronomy, and the theory of music. The theorem now known as Pythagoras's theorem was known to the Babylonians 1000 years earlier but he may have been the first to prove it. 30
31 r 2 =x 2 y 2 y x 31
32 r= x 2 y 2 y x 32
33 r= 4 m 2 3m 2 = 16 m 2 9m 2 = 25m 2 =5m r y=3 m x=4 m 33
34 r= 6 m 2 7m 2 = 36 m 2 49m 2 = 8 2 =9.22m r y=7m x=6 m 34
35 r y sin = y r cos = x r x tan = y x r= x 2 y 2 35
36 hyp opp sin = opp hyp cos = adj hyp adj tan = opp adj 36
37 j Vector Notation R= A B R=4m i 3 m j 3 m i 4 m R = 4m 2 3 m 2 = 2 2 =5m tan = opp =tan adj 1 3m 4m =36.87o 37
38 j R= A B R=4m i 3 m j o Vector Notation 3 m i 4 m R = 4m 2 3 m 2 = 2 2 =5m tan = opp =tan adj 1 3m 4m =36.87o 38
39 j R=10 40 o Vector Notation R =10 m R y R =40 o i R x 39
40 j R=10 40 o Vector Notation R =10 m R y R =40 o i R x cos = adj hyp cos R = R x R R x = R cos R =10 m cos 40 o =7.66m 40
41 j R=10 40 o Vector Notation R =10 m R y R =40 o R x =7.66 m sin = opp hyp i sin R = R y R R y = R sin R =10m sin 40 o =6.43m 41
42 j Vector Notation R =10 m R y =6.43m R =40 o R x =7.66 m i R=10 40 o R=R x i R y j=7.66 m i 6.43m j 42
43 j Vector Notation Check: R = R x 2 R y 2 R = 7.66 m m 2 =10 m R =10 m R =40 o R x =7.66 m R=10 40 o R y =6.43m i tan = R y R x 6.43 m =tan m =40o R=R x i R y j=7.66 m i 6.43m j 43
44 Vector Notation II A y =4 m j I A A= A x i A y j=3m i 4 m j A x =3 m i III IV 44
45 Vector Notation II A y =4 m j I A A= A x i A y j=3m i 4 m j A x =3 m i III IV A = 3m 2 4m 2 = A =tan 1 4 m 3 m =53.13o 45
46 Vector Notation II A y =4 m j I A A= A x i A y j=3m i 4 m j A= A =5m@53.13 o A A x =3 m i III IV A = 3m 2 4m 2 = A =tan 1 4 m 3 m =53.13o 46
47 Vector Notation II j I B B y =2m B=B x i B y j= 4m i 2m j B x =4 m B i III IV 47
48 Vector Notation II j I B B y =2m B=B x i B y j= 4m i 2m j B x = 4 m B i B = 4m 2 2m 2 =4.47m III IV 48
49 Vector Notation II j I B B y =2m B=B x i B y j= 4m i 2m j B x = 4 m B B ' i III IV B = 4m 2 2m 2 =4.47m B =tan 1 2m 4 m = 26.57o????? 49
50 Vector Notation II j I B B x = 4 m III B y =2m B IV B ' B=B x i B y j= 4m i 2m j i =180 o ' B B =180 o o = o B B = 4m 2 2m 2 =4.47m B =tan 1 2m 4 m = 26.57o????? 50
51 Vector Notation j II I B=B x i B y j= 4m i 2 m j B= B =4.47m@ o B B y =2m B x = 4 m B B ' i =180 o ' B B B =180 o o = o III IV B = 4m 2 2m 2 =4.47m B =tan 1 2m 4 m = 26.57o????? 51
52 Vector Notation j II I C=C x i C y j= 3m i 6 m j C x = 3m C i C C y = 6 m III IV 52
53 Vector Notation j II C C=C x i C y j= 3m i 6 m j C x = 3m C i C C y = 6 m III IV C = 3m 2 6m 2 =6.71m C =tan 1 6m 3 m =71.57o????? 53
54 Vector Notation j II I C=C x i C y j= 3m i 6 m j C x = 3m C C ' i C =180 o C ' C C y = 6 m C =180 o o = o III IV C = 3m 2 6m 2 =6.71m C =tan 1 6m 3 m =71.57o????? 54
55 Vector Notation j II I C=C x i C y j= 3m i 6 m j C= C =6.71m@ o C x = 3m C C ' i C =180 o C ' C C y = 6 m C =180 o o = o III IV C = 3m 2 6m 2 =6.71m C =tan 1 6m 3 m =71.57o????? 55
56 Vector Notation j II I D=D x i D y j=3m i 3 m j D= D = o D D x =3 m i D y = 3 m D III IV D = 3m 2 3m 2 =4.24 m D =tan 1 3m 3m = 45o????? 56
57 Vector Notation j II I D=D x i D y j=3m i 3 m j D= D = o D D y = 3 m D ' D x =3 m D i III IV D = 3m 2 3m 2 =4.24 m D =tan 1 3m 3m = 45o????? 57
58 Vector Notation II j I D=D x i D y j=3m i 3 m j D= D = o = o D D y = 3 m D ' D x =3 m D i D =360 o C ' D =360 o 45 o =315 o III IV D = 3m 2 3m 2 =4.24 m D =tan 1 3m 3m = 45o????? 58
59 Adding Vectors 59
60 Adding Vectors A=5m i 0 m j B=0m i 6 m j B A 60
61 Adding Vectors C B A=5m i 0 m j B=0m i 6 m j C= A B=5m i 6 m j A 61
62 Adding Vectors C B A=5m i 0 m j B=0m i 6 m j C= A B=5m i 6 m j A C = 5m 2 6m 2 =7.81 m C =tan 1 6m =50.19o 62
63 Adding Vectors B A 63
64 Adding Vectors A=5m i 0m j B=3m i 5m j B B y A A x B x 64
65 Adding Vectors A=5m i 0m j B=3m i 5m j C= A B=8m i 5m j C B A C = 8m 2 5m 2 =9.43m C =tan 1 5m 8 m =32.00o 65
66 Adding Vectors Vectors may be moved so that the tail of each is at the origin. B A 66
67 Adding Vectors B A 67
68 Adding Vectors C=C x i C y j B C A 68
69 Adding Vectors C=C x i C y j B C C y = A C x =8 m 69
70 Adding Vectors C=C x i C y j C=8m i 5m j B C C y = A C x =8 m 70
71 Adding Vectors C=C x i C y j C=8m i 5m j B C C y = A C x =8 m C = 8m 2 5m 2 =9.43m C =tan 1 5m 8 m =32.00o 71
72 Adding Vectors B A 72
73 Adding Vectors A=5m i 0m j B= 5m i j B A 73
74 Adding Vectors A=5m i 0m j B= 5m i j B A 74
75 Adding Vectors A=5m i 0m j B= 5m i j B C A 75
76 Adding Vectors A=5m i 0m j B= 5m i j C= A B=0m i j B C A C = 0m 2 5m 2 =5.00m C =90.00 o 76
77 Adding Vectors B A 77
78 Adding Vectors B A 78
79 Adding Vectors B A 79
80 Adding Vectors B C= A B C=C x i C y j C=2m i 8m j A C = 2 m 2 8m 2 =8.2 C =tan 1 8m 2 m =75.96o 80
81 Adding Vectors A=7m i 3m j B= 5m i j B A 81
82 Adding Vectors A=7m i 3m j B= 5m i j C B A 82
83 Adding Vectors A=7m i 3m j B= 5m i j C C= A B=2 m i 8 m j B C A C = 2 m 2 8 m 2 =8.2 C =tan 1 8m 2 m =75.96o 83
84 Adding Vectors B C A=7m i 3m j B= 5m i j C=4 m i 2m j A 84
85 Adding Vectors A=7m i 3m j C B= 5m i j C=4 m i 2m j B D D= A B C=6m i 6 m j A 85
86 Adding Vectors A=7m i 3m j B= 5m i j C=4 m i 2m j D= A B C=6m i 6 m j B A C 86
87 Adding Vectors A=7m i 3m j B= 5m i j C=4 m i 2m j A B D= A B C=6m i 6 m j B A C 87
88 Adding Vectors A B A=7m i 3m j B= 5m i j C=4 m i 2m j D= A B C=6m i 6 m j A B C C 88
89 Adding Vectors A=7m i 3m j B= 5m i j C=4 m i 2m j D= A B C=6m i 6 m j A B C= D C 89
90 Adding Vectors B C F A D E 90
91 Adding Vectors A=5m i 2 m j B C F A D E 91
92 Adding Vectors B C A=5m i 2 m j B=3m i 6m j F A D E 92
93 Adding Vectors B C A=5m i 2 m j B=3m i 6m j C=0m i 3 m j F A D E 93
94 Adding Vectors B C A=5m i 2 m j B=3m i 6m j C=0m i 3 m j D= 8m i 10 m j F A D E 94
95 Adding Vectors B C A=5m i 2 m j B=3m i 6m j C=0m i 3 m j D= 8m i 10 m j F A D E= i 0 m j E 95
96 Adding Vectors B C A=5m i 2 m j B=3m i 6m j C=0m i 3 m j D= 8m i 10 m j F A D E= i 0 m j F= 3 m i 10 m j E 96
97 Adding Vectors B C A=5m i 2 m j B=3m i 6m j C=0m i 3 m j D= 8m i 10 m j F R A D E= i 0 m j F= 3 m i 10 m j R= 2 m i 5m j E 97
98 Adding Vectors B C A=5m i 2 m j B=3m i 6m j C=0m i 3 m j D= 8m i 10 m j F R A D E= i 0 m j F= 3 m i 10 m j R= 2 m i 5m j E R = 2 m 2 2 =5.39 m R =tan 1 5m 2m = 68.20o 180 o = o 98
99 Adding Vectors F B E A C D 99
100 Adding Vectors F B E A C D 100
101 Adding Vectors F D 101
102 Adding Vectors F D 102
103 Adding Vectors F R R= 2 m i 5m j D 103
104 Adding Vectors F R R= 2 m i 5m j D 104
105 More Vectors: s Displacement [ s]=m Distance between the starting point and final point and direction. v Velocity [ v]=m/ s Speed and direction. The time derivative of position a Acceleration [ a]=m/s 2 The time derivative of velocity 105
106 x=100 m Tugboat with broken rudder. Can only go straight. It takes ten seconds to cross calm lake. v x = x t =100 m 10 s =10 m/s 106
107 x=100 m Tugboat with broken rudder. Can only go straight. It takes ten seconds to cross calm lake. v x =10m/ s v x = x t =100 m 10 s =10 m/s 107
108 x=100 m Tugboat with broken rudder. Can only go straight. It takes ten seconds to cross lake. Now consider strong current. v x =10m/ s x=100 m v y =/s y=v y t= /s 10 s =50 m 108
109 x=100 m Tugboat with broken rudder. Can only go straight. It takes ten seconds to cross lake. Now consider strong current. v y=50 m x=100 m v y =/s 109
110 x=100 m Tugboat with broken rudder. Can only go straight. It takes ten seconds to cross lake. Now consider strong current. v x=100 m v y =/s y=50 m v=v x i v y j v=10 m/s i 5m/s j 110
111 x=100 m Tugboat with broken rudder. Can only go straight. It takes ten seconds to cross lake. Now consider strong current. v x=100 m v y =/s y=50 m v=v x i v y j v=10m/s i / s j v = 10 m/s 2 /s 2 =11.18 m/s /s =tan 1 10 m/s =26.57o 111
112 x=100 m Tugboat with broken rudder. Can only go straight. It takes ten seconds to cross lake. Now consider strong current. v x=100 m v y =/s y=50 m o r= x 2 y 2 r= 100 m 2 50 m 2 = m 112
113 x=100 m Tugboat with broken rudder. Can only go straight. It takes ten seconds to cross lake. Now consider strong current. v x=100 m v y =/s y=50 m v=11.18 m/ s@26.57 o r= m v= r t = m =11.18 m/ s 10 s 113
114 x=100 m Tugboat with broken rudder. Can only go straight. It takes ten seconds to cross lake. Now consider strong current. v x=100 m y=50 m v y =/s v =11.18 m/ s =26.57 o v x =10 m/s v y =/s v=11.18 m/ s@26.57 o r= m v= r t = m =11.18 m/ s 10 s 114
115 Adding Vectors v=17.20 o 10m/ s 10m/ s 10m/ s 10m/ s 115
116 Adding Vectors v y = v sin v y =17.20 m/s sin o v y =14 m/s 10m/ s v=17.20m/s@54.46 o 10m/ s 10m/ s 10m/ s v x = v cos v x =17.20 m/s cos54.46 o v x =10 m/s 116
Precalculus Lesson 6.1: Angles and Their Measure Lesson 6.2: A Unit Circle Approach Part 2
Precalculus Lesson 6.1: Angles and Their Measure Lesson 6.2: A Unit Circle Approach Part 2 Lesson 6.2 Before we look at the unit circle with respect to the trigonometric functions, we need to get some
More informationChapter 8 Scalars and vectors
Chapter 8 Scalars and vectors Heinemann Physics 1 4e Section 8.1 Scalars and vectors Worked example: Try yourself 8.1.1 DESCRIBING VECTORS IN ONE DIMENSION west east + 50 N Describe the vector using: a
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 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 informationy d y b x a x b Fundamentals of Engineering Review Fundamentals of Engineering Review 1 d x y Introduction - Algebra Cartesian Coordinates
Fundamentals of Engineering Review RICHARD L. JONES FE MATH REVIEW ALGEBRA AND TRIG 8//00 Introduction - Algebra Cartesian Coordinates Lines and Linear Equations Quadratics Logs and exponents Inequalities
More informationLesson 7. Chapter 3: Two-Dimensional Kinematics COLLEGE PHYSICS VECTORS. Video Narrated by Jason Harlow, Physics Department, University of Toronto
COLLEGE PHYSICS Chapter 3: Two-Dimensional Kinematics Lesson 7 Video Narrated by Jason Harlow, Physics Department, University of Toronto VECTORS A quantity having both a magnitude and a direction is called
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 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 informationHere is a sample problem that shows you how to use two different methods to add twodimensional
LAB 2 VECTOR ADDITION-METHODS AND PRACTICE Purpose : You will learn how to use two different methods to add vectors. Materials: Scientific calculator, pencil, unlined paper, protractor, ruler. Discussion:
More informationCambridge International Examinations CambridgeOrdinaryLevel
Cambridge International Examinations CambridgeOrdinaryLevel * 2 5 4 0 0 0 9 5 8 5 * ADDITIONAL MATHEMATICS 4037/12 Paper1 May/June 2015 2 hours CandidatesanswerontheQuestionPaper. NoAdditionalMaterialsarerequired.
More information1-dimensional: origin. Above is a vector drawing that represents the displacement of the point from zero. point on a line: x = 2
I. WHT IS VECTO? UNIT XX: VECTOS VECTO is a variable quantity consisting of two components: o o MGNITUDE: How big? This can represent length, pressure, rate, and other quantities DIECTION: Which way is
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 informationUnit IV: Introduction to Vector Analysis
Unit IV: Introduction to Vector nalysis s you learned in the last unit, there is a difference between speed and velocity. Speed is an example of a scalar: a quantity that has only magnitude. Velocity is
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 informationCHAPTER 71 NUMERICAL INTEGRATION
CHAPTER 7 NUMERICAL INTEGRATION EXERCISE 8 Page 759. Evaluate using the trapezoidal rule, giving the answers correct to decimal places: + d (use 8 intervals) + = 8 d, width of interval =.5.5.5.75.5.65.75.875.
More informationUnit Circle. Return to. Contents
Unit Circle Return to Table of Contents 32 The Unit Circle The circle x 2 + y 2 = 1, with center (0,0) and radius 1, is called the unit circle. Quadrant II: x is negative and y is positive (0,1) 1 Quadrant
More informationKINEMATICS REVIEW VECTOR ALGEBRA - SUMMARY
1 KINEMATICS REVIEW VECTOR ALGEBRA - SUMMARY Magnitude A numerical value with appropriate units. Scalar is a quantity that is completely specified by magnitude. Vector requires both, magnitude and direction
More informationPre-Calculus II: Trigonometry Exam 1 Preparation Solutions. Math&142 November 8, 2016
Pre-Calculus II: Trigonometry Exam 1 Preparation Solutions Math&1 November 8, 016 1. Convert the angle in degrees to radian. Express the answer as a multiple of π. a 87 π rad 180 = 87π 180 rad b 16 π rad
More informationAP PHYSICS B SUMMER ASSIGNMENT: Calculators allowed! 1
P PHYSICS SUMME SSIGNMENT: Calculators allowed! 1 The Metric System Everything in physics is measured in the metric system. The only time that you will see English units is when you convert them to metric
More informationPhysics Skills (a.k.a. math review)
Physics Skills (a.k.a. math review) PART I. SOLVING EQUATIONS Solve the following equations for the quantity indicated. 1. y = 1 at Solve for t. x = vot + 1 at Solve for v o 3. v = ax Solve for x v 4.
More informationBeauchamp College Year 11/12 - A- Level Transition Work. Physics.
Beauchamp College Year 11/1 - A- Level Transition Work Physics Gareth.butcher@beauchamp.org.uk Using S.I. units Specification references.1. a) b) c) d) M0.1 Recognise and make use of appropriate units
More informationPhysics 20 Lesson 10 Vector Addition
Physics 20 Lesson 10 Vector Addition I. Vector Addition in One Dimension (It is strongly recommended that you read pages 70 to 75 in Pearson for a good discussion on vector addition in one dimension.)
More informationTrigonometry Trigonometry comes from the Greek word meaning measurement of triangles Angles are typically labeled with Greek letters
Trigonometry Trigonometry comes from the Greek word meaning measurement of triangles Angles are typically labeled with Greek letters α( alpha), β ( beta), θ ( theta) as well as upper case letters A,B,
More informationv v y = v sinθ Component Vectors:
Component Vectors: Recall that in order to simplify vector calculations we change a complex vector into two simple horizontal (x) and vertical (y) vectors v v y = v sinθ v x = v cosθ 1 Component Vectors:
More informationCore Mathematics 2 Trigonometry
Core Mathematics 2 Trigonometry Edited by: K V Kumaran Email: kvkumaran@gmail.com Core Mathematics 2 Trigonometry 2 1 Trigonometry Sine, cosine and tangent functions. Their graphs, symmetries and periodicity.
More informationAP Physics 1 First Semester Final Exam Review
AP Physics First Semester Final Exam Review Chapters and. Know the SI Units base units.. Be able to use the factor-label method to convert from one unit to another (ex: cm/s to m/year) 3. Be able to identify
More informationUnit 4 Review. inertia interaction pair net force Newton s first law Newton s second law Newton s third law position-time graph
Unit 4 Review Vocabulary Review Each term may be used once. acceleration constant acceleration constant velocity displacement force force of gravity friction force inertia interaction pair net force Newton
More informationMain Ideas in Class Today
Main Ideas in Class Today After today, you should be able to: Understand vector notation Use basic trigonometry in order to find the x and y components of a vector (only right triangles) Add and subtract
More informationReview Exercises for Chapter 4
0 Chapter Trigonometr Review Eercises for Chapter. 0. radian.. radians... The angle lies in Quadrant II. (c) Coterminal angles: Quadrant I (c) 0 The angle lies in Quadrant II. (c) Coterminal angles: 0.
More informationAP Physics C: UNIT CONVERSION
AP Physics C: UNIT CONVERSION 1. Convert each of the following measurements into the specified units. a. 42.3 cm = 423 mm d. 0.023 mm = 0.23 cm 1 cm = 10 mm b. 6.2 pm = _0.0000000000062_ m e. 214 µm =
More informationAll E Maths Formulas for O levels E Maths by Ethan Wu
All E Maths Formulas for O levels E Maths by Ethan Wu Chapter 1: Indices a 5 = a x a x a x a x a a m a n = a m + n a m a n = a m n (a m ) n = a m n (ab) n = a n b n ( a b )n = an b n a 0 = 1 a -n = 1 a
More informationCreated by T. Madas CALCULUS KINEMATICS. Created by T. Madas
CALCULUS KINEMATICS CALCULUS KINEMATICS IN SCALAR FORM Question (**) A particle P is moving on the x axis and its acceleration a ms, t seconds after a given instant, is given by a = 6t 8, t 0. The particle
More informationTOPICS, TERMS and FORMULAS, ASTR 402 (Fall 11)
TOPICS, TERMS and FORMULAS, ASTR 402 (Fall 11) Here is the set of topics and terms for the first quiz. I PROMISE the next set will have much less math! If you don t have a calculator, you can get sines
More informationBROAD RUN HIGH SCHOOL AP PHYSICS C: MECHANICS SUMMER ASSIGNMENT
AP Physics C - Mechanics Due: September 2, 2014 Name Time Allotted: 8-10 hours BROAD RUN HIGH SCHOOL AP PHYSICS C: MECHANICS SUMMER ASSIGNMENT 2014-2015 Teacher: Mrs. Kent Textbook: Physics for Scientists
More informationChapter 8 Test Wednesday 3/28
Chapter 8 Test Wednesday 3/28 Warmup Pg. 487 #1-4 in the Geo book 5 minutes to finish 1 x = 4.648 x = 40.970 x = 6149.090 x = -5 What are we learning today? Pythagoras The Rule of Pythagoras Using Pythagoras
More informationYou must have: Ruler graduated in centimetres and millimetres, protractor, compasses, pen, HB pencil, eraser, calculator. Tracing paper may be used.
Write your name here Surname Other names Pearson Edexcel Certificate Pearson Edexcel International GCSE Mathematics A Paper 3H Thursday 26 May 2016 Morning Time: 2 hours Centre Number Candidate Number
More informationMathematics GCSE Higher Tier Taster Pages
Question 14 (June 2011 4306/1H) a) on the cumulative frequency diagram you can work out the lower quartile, median and upper quartile. These have been got by using the dashed red lines. Draw them across
More informationIB Math SL Year 2 Name Date Lesson 10-4: Displacement, Velocity, Acceleration Revisited
Name Date Lesson 10-4: Displacement, Velocity, Acceleration Revisited Learning Goals: How do you apply integrals to real-world scenarios? Recall: Linear Motion When an object is moving, a ball in the air
More informationSOH CAH TOA. b c. sin opp. hyp. cos adj. hyp a c. tan opp. adj b a
SOH CAH TOA sin opp hyp b c c 2 a 2 b 2 cos adj hyp a c tan opp adj b a Trigonometry Review We will be focusing on triangles What is a right triangle? A triangle with a 90º angle What is a hypotenuse?
More informationDecimals. can be written as a terminating. factor. (1 mark) (1 mark) (2 marks) (b) 25. (1 mark) (1 mark) (1 mark)
Nailed it!nailed it!number HadNearly a go there Nearly there Had a look NUMBER Decimals Factors, multiples and primes Write thesemultiples s in order of size. Start withprimes the smallest. Factors and
More informationPythagoras Theorem. What it is: When to use: What to watch out for:
Pythagoras Theorem a + b = c Where c is the length of the hypotenuse and a and b are the lengths of the other two sides. Note: Only valid for right-angled triangles! When you know the lengths of any two
More information15 x. Substitute. Multiply. Add. Find the positive square root.
hapter Review.1 The Pythagorean Theorem (pp. 3 70) Dynamic Solutions available at igideasmath.com Find the value of. Then tell whether the side lengths form a Pythagorean triple. c 2 = a 2 + b 2 Pythagorean
More informationb) (6) What is the volume of the iron cube, in m 3?
General Physics I Exam 4 - Chs. 10,11,12 - Fluids, Waves, Sound Nov. 14, 2012 Name Rec. Instr. Rec. Time For full credit, make your work clear to the grader. Show formulas used, essential steps, and results
More informationUniform Circular Motion AP
Uniform Circular Motion AP Uniform circular motion is motion in a circle at the same speed Speed is constant, velocity direction changes the speed of an object moving in a circle is given by v circumference
More informationName. Welcome to AP Physics. I am very excited that you have signed up to take the AP Physics class.
Name P Physics Summer ssignment Fall 013-014 Welcome to P Physics. I am very excited that you have signed up to take the P Physics class. You may ask I sure would why a summer packet? There is so much
More informationAP Physics 1 Mr. Perkins June 2014 SUMMER WORK FOR AP PHYSICS 1 STUDENTS
AP Physics 1 Mr. Perkins June 2014 SUMMER WORK FOR 2014-2015 AP PHYSICS 1 STUDENTS 1. Read Chapter 1 of Textbook (Giancoli pp.1-17). Make a list of questions about any topics you would like clarified on
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 informationMTH 112: Elementary Functions
1/19 MTH 11: Elementary Functions Section 6.6 6.6:Inverse Trigonometric functions /19 Inverse Trig functions 1 1 functions satisfy the horizontal line test: Any horizontal line crosses the graph of a 1
More information1 - Astronomical Tools
ASTR 110L 1 - Astronomical Tools Purpose: To learn fundamental tools astronomers use on a daily basis. Turn in all 13 problems on a separate sheet. Due in one week at the start of class. Units All physical
More informationThe region enclosed by the curve of f and the x-axis is rotated 360 about the x-axis. Find the volume of the solid formed.
Section A ln. Let g() =, for > 0. ln Use the quotient rule to show that g ( ). 3 (b) The graph of g has a maimum point at A. Find the -coordinate of A. (Total 7 marks) 6. Let h() =. Find h (0). cos 3.
More informationb) (6) With 10.0 N applied to the smaller piston, what pressure force F 2 (in newtons) is produced on the larger piston?
General Physics I Exam 4 - Chs. 10,11,12 - Fluids, Waves, Sound Nov. 17, 2010 Name Rec. Instr. Rec. Time For full credit, make your work clear to the grader. Show formulas used, essential steps, and results
More informationYou must have: Ruler graduated in centimetres and millimetres, protractor, compasses, pen, HB pencil, eraser, calculator. Tracing paper may be used.
Write your name here Surname Other names Edexcel Certificate Edexcel International GCSE Mathematics A Paper 3H Friday 10 May 2013 Afternoon Time: 2 hours Centre Number Candidate Number Higher Tier Paper
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 informationMathematics IGCSE Higher Tier, November /4H (Paper 4H)
Link to examining board: http://www.edexcel.com The question paper associated with these solutions is available to download for free from the Edexcel website. The navigation around the website sometimes
More information<v140988_ph_001> Engineering Principles 1 DRAFT
1 Getting to know your unit Assessment This unit is externally assessed using an unseen paper-based examination that is marked by Pearson. How you will be assessed To make an effective
More informationMEI STRUCTURED MATHEMATICS 4763
OXFORD CAMBRIDGE AND RSA EXAMINATIONS Advanced Subsidiary General Certificate of Education Advanced General Certificate of Education MEI STRUCTURED MATHEMATICS 76 Mechanics Monday MAY 006 Morning hour
More information. d. v A v B. e. none of these.
General Physics I Exam 3 - Chs. 7,8,9 - Momentum, Rotation, Equilibrium Oct. 28, 2009 Name Rec. Instr. Rec. Time For full credit, make your work clear to the grader. Show the formulas you use, the essential
More informationYou must have: Ruler graduated in centimetres and millimetres, protractor, compasses, pen, HB pencil, eraser, calculator. Tracing paper may be used.
Write your name here Surname Other names Pearson Edexcel International GCSE Mathematics A Paper 3HR Friday 10 January 2014 Morning Time: 2 hours Centre Number Candidate Number Higher Tier Paper Reference
More informationWorksheet for Exploration 10.1: Constant Angular Velocity Equation
Worksheet for Exploration 10.1: Constant Angular Velocity Equation By now you have seen the equation: θ = θ 0 + ω 0 *t. Perhaps you have even derived it for yourself. But what does it really mean for the
More informationMathematics Revision Guide. Shape and Space. Grade C B
Mathematics Revision Guide Shape and Space Grade C B 1 A of = b h 2 Area 6cm = 10 6 2 = 60 2 8cm = 30cm 2 6cm 12cm A of = (a+b) h 2 = (6+12) 5 2 = (18) 5 2 = 90 2 = 4 2 7cm 1 6cm A of = π r r = π 6 6 =
More informationMathematics IGCSE Higher Tier, June /4H (Paper 4H)
Link to examining board: http://www.edexcel.com The question paper associated with these solutions is available to download for free from the Edexcel website. The navigation around the website sometimes
More informationn power Name: NOTES 2.5, Date: Period: Mrs. Nguyen s Initial: LESSON 2.5 MODELING VARIATION
NOTES 2.5, 6.1 6.3 Name: Date: Period: Mrs. Nguyen s Initial: LESSON 2.5 MODELING VARIATION Direct Variation y mx b when b 0 or y mx or y kx y kx and k 0 - y varies directly as x - y is directly proportional
More information1. AP Physics math review
1. AP Physics math review PART I. SOLVING EQUATIONS Solve the following equations for the quantity indicated. 1. y = 1 at Solve for t. x = vot + 1 at Solve for v o 3. v = ax Solve for x v 4. a = f v t
More information2- Scalars and Vectors
2- Scalars and Vectors Scalars : have magnitude only : Length, time, mass, speed and volume is example of scalar. v Vectors : have magnitude and direction. v The magnitude of is written v v Position, displacement,
More informationVectors. However, cartesian coordinates are really nothing more than a way to pinpoint an object s position in space
Vectors Definition of Scalars and Vectors - A quantity that requires both magnitude and direction for a complete description is called a vector quantity ex) force, velocity, displacement, position vector,
More informationYou must have: Ruler graduated in centimetres and millimetres, protractor, compasses, pen, HB pencil, eraser, calculator. Tracing paper may be used.
Write your name here Surname Other names Pearson Edexcel International GCSE Mathematics A Paper 4HR Centre Number Monday 12 January 2015 Afternoon Time: 2 hours Candidate Number Higher Tier Paper Reference
More informationLondon Examinations IGCSE
Centre No. Candidate No. Surname Signature Initial(s) Paper Reference(s) 4400/4H London Examinations IGCSE Mathematics Paper 4H Higher Tier Friday 18 May 2007 Afternoon Time: 2 hours Materials required
More informationPHYSICS 1 REVIEW PACKET
PHYSICS 1 REVIEW PACKET Powers of Ten Scientific Notation and Prefixes Exponents on the Calculator Conversions A Little Trig Accuracy and Precision of Measurement Significant Figures Motion in One Dimension
More information10.1 Three Dimensional Space
Math 172 Chapter 10A notes Page 1 of 12 10.1 Three Dimensional Space 2D space 0 xx.. xx-, 0 yy yy-, PP(xx, yy) [Fig. 1] Point PP represented by (xx, yy), an ordered pair of real nos. Set of all ordered
More informationLondon Examinations IGCSE. Wednesday 8 November 2006 Morning
Centre No. Candidate No. Surname Signature Initial(s) Paper Reference(s) 4400/4H London Examinations IGCSE Mathematics Paper 4H Higher Tier Wednesday 8 November 2006 Morning Time: 2 hours Materials required
More informationDisplacement, Velocity and Acceleration in one dimension
Displacement, Velocity and Acceleration in one dimension In this document we consider the general relationship between displacement, velocity and acceleration. Displacement, velocity and acceleration are
More informationMath 30-1 Trigonometry Prac ce Exam 4. There are two op ons for PP( 5, mm), it can be drawn in SOLUTIONS
SOLUTIONS Math 0- Trigonometry Prac ce Exam Visit for more Math 0- Study Materials.. First determine quadrant terminates in. Since ssssss is nega ve in Quad III and IV, and tttttt is neg. in II and IV,
More informationNeed to have some new mathematical techniques to do this: however you may need to revise your basic trigonometry. Basic Trigonometry
Kinematics in Two Dimensions Kinematics in 2-dimensions. By the end of this you will 1. Remember your Trigonometry 2. Know how to handle vectors 3. be able to handle problems in 2-dimensions 4. understand
More informationBe prepared to take a test covering the whole assignment in September. MATH REVIEW
P- Physics Name: Summer 013 ssignment Date Period I. The attached pages contain a brief review, hints, and example problems. It is hoped that combined with your previous math knowledge this assignment
More informationYou must have: Ruler graduated in centimetres and millimetres, protractor, compasses, pen, HB pencil, eraser, calculator. Tracing paper may be used.
Write your name here Surname Other names Edexcel IGCSE Mathematics A Paper 1F Monday 6 June 2011 Afternoon Time: 2 hours Centre Number Candidate Number Foundation Tier Paper Reference 4MA0/1F You must
More informationI. Degrees and Radians minutes equal 1 degree seconds equal 1 minute. 3. Also, 3600 seconds equal 1 degree. 3.
0//0 I. Degrees and Radians A. A degree is a unit of angular measure equal to /80 th of a straight angle. B. A degree is broken up into minutes and seconds (in the DMS degree minute second sstem) as follows:.
More informationPart I, Number Systems CS131 Mathematics for Computer Scientists II Note 3 VECTORS
CS131 Part I, Number Systems CS131 Mathematics for Computer Scientists II Note 3 VECTRS Vectors in two and three dimensional space are defined to be members of the sets R 2 and R 3 defined by: R 2 = {(x,
More informationLecture 1a: Satellite Orbits
Lecture 1a: Satellite Orbits Meteorological Satellite Orbits LEO view GEO view Two main orbits of Met Satellites: 1) Geostationary Orbit (GEO) 1) Low Earth Orbit (LEO) or polar orbits Orbits of meteorological
More informationLondon Examinations IGCSE
Centre No. Candidate No. Paper Reference 4 4 0 0 4 H Surname Signature Paper Reference(s) 4400/4H London Examinations IGCSE Mathematics Paper 4H Higher Tier Wednesday 12 November 2008 Morning Time: 2 hours
More informationHigher Mathematics Course Notes
Higher Mathematics Course Notes Equation of a Line (i) Collinearity: (ii) Gradient: If points are collinear then they lie on the same straight line. i.e. to show that A, B and C are collinear, show that
More informationMTH 133: Plane Trigonometry
MTH 133: Plane Trigonometry The Trigonometric Functions Right Angle Trigonometry Thomas W. Judson Department of Mathematics & Statistics Stephen F. Austin State University Fall 2017 Plane Trigonometry
More informationREQUIRED Assignment (June 15 th August 24th)
AP Physics C - Mechanics Due Date: August 24th Name BROAD RUN HIGH SCHOOL AP PHYSICS C: MECHANICS SUMMER ASSIGNMENT 2017-2018 Teacher: Mr. Manning Textbook: Physics for Scientists and Engineers, 9 th Edition,
More information1. Joseph runs along a long straight track. The variation of his speed v with time t is shown below.
Kinematics 1. Joseph runs along a long straight track. The variation of his speed v with time t is shown below. After 25 seconds Joseph has run 200 m. Which of the following is correct at 25 seconds? Instantaneous
More informationToday: Scalars and vectors Coordinate systems, Components Vector Algebra
PHY131H1F - Class 6 Today: Scalars and vectors Coordinate systems, Components Vector Algebra Clicker Question The ball rolls up the ramp, then back down. Which is the correct acceleration graph? [Define
More informationDEVIL PHYSICS THE BADDEST CLASS ON CAMPUS IB PHYSICS
DEVIL PHYSICS THE BADDEST CLASS ON CAMPUS IB PHYSICS LSN 2-1, KINEMATICS Questions From Reading Activity? Assessment Statements Topic 2.1, Kinematics: Define displacement, velocity, speed, and acceleration.
More informationRefresher course on Electrical fundamentals (Basics of A.C. Circuits) by B.M.Vyas
Refresher course on Electrical fundamentals (Basics of A.C. Circuits) by B.M.Vyas A specifically designed programme for Da Afghanistan Breshna Sherkat (DABS) Afghanistan 1 Areas Covered Under this Module
More informationTrigonometric Functions. Copyright Cengage Learning. All rights reserved.
4 Trigonometric Functions Copyright Cengage Learning. All rights reserved. 4.3 Right Triangle Trigonometry Copyright Cengage Learning. All rights reserved. What You Should Learn Evaluate trigonometric
More informationPaper Reference. London Examinations IGCSE Mathematics Paper 3H. Higher Tier. Thursday 15 May 2008 Morning Time: 2 hours
Centre No. Candidate No. Paper Reference 4 4 0 0 3 H Surname Signature Paper Reference(s) 4400/3H London Examinations IGCSE Mathematics Paper 3H Higher Tier Thursday 15 May 2008 Morning Time: 2 hours Initial(s)
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 informationYou must have: Ruler graduated in centimetres and millimetres, protractor, compasses, pen, HB pencil, eraser, calculator. Tracing paper may be used.
Write your name here Surname Other names Edexcel International GCSE Centre Number Candidate Number Mathematics A Paper 3HR Friday 10 May 2013 Afternoon Time: 2 hours Higher Tier Paper Reference 4MA0/3HR
More information10.2 Introduction to Vectors
Arkansas Tech University MATH 2934: Calculus III Dr. Marcel B Finan 10.2 Introduction to Vectors In the previous calculus classes we have seen that the study of motion involved the introduction of a variety
More informationLondon Examinations IGCSE
Centre No. Candidate No. Paper Reference 4 4 0 0 3 H Surname Signature Paper Reference(s) 4400/3H London Examinations IGCSE Mathematics Paper 3H Higher Tier Thursday 11 November 2010 Morning Time: 2 hours
More informationYou must have: Ruler graduated in centimetres and millimetres, protractor, compasses, pen, HB pencil, eraser, calculator. Tracing paper may be used.
Write your name here Surname Other names Edexcel Certificate Edexcel International GCSE Mathematics A Paper 1F Friday 11 January 2013 Morning Time: 2 hours Centre Number Candidate Number Foundation Tier
More informationLesson 15: Rearranging Formulas
Exploratory Challenge Rearranging Familiar Formulas 1. The area AA of a rectangle is 25 in 2. The formula for area is AA = llll. A. If the width ll is 10 inches, what is the length ll? AA = 25 in 2 ll
More informationPhysics 20 Lesson 11 Vector Addition Components
Phsics 20 Lesson 11 Vector ddition Components In Lesson 10 we learned how to add vectors which were perpendicular to one another using vector diagrams, Pthagorean theor, and the tangent function. What
More informationThe American School of Marrakesh. AP Calculus AB Summer Preparation Packet
The American School of Marrakesh AP Calculus AB Summer Preparation Packet Summer 2016 SKILLS NEEDED FOR CALCULUS I. Algebra: *A. Exponents (operations with integer, fractional, and negative exponents)
More informationMOTION IN TWO OR THREE DIMENSIONS
MOTION IN TWO OR THREE DIMENSIONS 3 Sections Covered 3.1 : Position & velocity vectors 3.2 : The acceleration vector 3.3 : Projectile motion 3.4 : Motion in a circle 3.5 : Relative velocity 3.1 Position
More informationYou must have: Ruler graduated in centimetres and millimetres, protractor, compasses, pen, HB pencil, eraser, calculator. Tracing paper may be used.
Write your name here Surname Other names Pearson Edexcel International GCSE Mathematics A Paper 3H Centre Number Monday 9 January 2017 Morning Time: 2 hours Candidate Number Higher Tier Paper Reference
More informationMTH 112: Elementary Functions
MTH 11: Elementary Functions F. Patricia Medina Department of Mathematics. Oregon State University Section 6.6 Inverse Trig functions 1 1 functions satisfy the horizontal line test: Any horizontal line
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 information