A Demonstrative Approach. Let’s say we need to find the vertical (V Y ) and horizontal (V X ) components of this here vector. The first step is to find.

Slides:



Advertisements
Similar presentations
Topic 1.3 Extended B - Components of motion Up to now we have considered objects moving in one dimension. However, most objects move in more than one.
Advertisements

Aim: How can we describe resultant force (net force)?
Trigonometry Right Angled Triangle. Hypotenuse [H]
Right Triangle Trigonometry
Trigonometric Ratios Please view this tutorial and answer the follow-up questions on loose leaf to turn in to your teacher.
1 7.2 Right Triangle Trigonometry In this section, we will study the following topics: Evaluating trig functions of acute angles using right triangles.
Glencoe Physics Ch 4 Remember…. When drawing vectors… length = magnitude (with scale) angle = direction of the vector quantity. When drawing and moving.
Copyright © Cengage Learning. All rights reserved. 6 Inverse Functions.
Richard J. Terwilliger by Let’s look at some examples.
Properties of Scalars and Vectors. Vectors A vector contains two pieces of information: specific numerical value specific direction drawn as arrows on.
Force Vectors. Vectors Have both a magnitude and direction Examples: Position, force, moment Vector Quantities Vector Notation Handwritten notation usually.
Working out an unknown side or angle in a right angled triangle. Miss Hudson’s Maths.
Chapter 1. Vectors and Coordinate Systems
Copyright © Cengage Learning. All rights reserved.
Trigonometry Chapters Theorem.
Basic Trigonometry.
Vectors and Vector Addition Honors/MYIB Physics. This is a vector.
Maths Methods Trigonometric equations K McMullen 2012.
ENGINEERING MECHANICS CHAPTER 2 FORCES & RESULTANTS
#3 NOTEBOOK PAGE 16 – 9/7-8/2010. Page 16 & Geometry & Trigonometry P19 #2 P19 # 4 P20 #5 P20 # 7 Wed 9/8 Tue 9/7 Problem Workbook. Write questions!
VECTORS v Fp Scalar quantities – that can be completely described by a number with the appropriate units. ( They have magnitude only. ) Such as length,
Topic 1 Pythagorean Theorem and SOH CAH TOA Unit 3 Topic 1.
1.3.1Distinguish between vector and scalar quantities and give examples of each Determine the sum or difference of two vectors by a graphical method.
Vectors - Fundamentals and Operations A vector quantity is a quantity which is fully described by both magnitude and direction.
Unit 1 – Physics Math Algebra, Geometry and Trig..
Vectors & Scalars Vectors are measurements which have both magnitude (size) and a directional component. Scalars are measurements which have only magnitude.
Forces in 2D Chapter Vectors Both magnitude (size) and direction Magnitude always positive Can’t have a negative speed But can have a negative.
Vector Quantities We will concern ourselves with two measurable quantities: Scalar quantities: physical quantities expressed in terms of a magnitude only.
PHYSICS: Vectors and Projectile Motion. Today’s Goals Students will: 1.Be able to describe the difference between a vector and a scalar. 2.Be able to.
CHAPTER 5 FORCES IN TWO DIMENSIONS
VECTORS. Pythagorean Theorem Recall that a right triangle has a 90° angle as one of its angles. The side that is opposite the 90° angle is called the.
Vectors and Two Dimensional Motion Chapter 3. Scalars vs. Vectors Vectors indicate direction ; scalars do not. Scalar – magnitude with no direction Vector.
Chapter 3 Vectors.
Chapter 3-2 Component Vectors. Pythagorean Theorem If two vectors are at a 90 0 angle, use the Pythagorean Theorem to find the resultant vector. C 2 =
Vectors Ch 3 Vectors Vectors are arrows Vectors are arrows They have both size and direction (magnitude & direction – OH YEAH!) They have both size and.
Chapter 4 Vector Addition When handwritten, use an arrow: When printed, will be in bold print: A When dealing with just the magnitude of a vector in print,
The process of vector addition is like following a treasure map. ARRRR, Ye best learn your vectors!
Vectors Vector: a quantity that has both magnitude (size) and direction Examples: displacement, velocity, acceleration Scalar: a quantity that has no.
The Right Triangle Right Triangle Pythagorean Theorem
Chapter 3–2: Vector Operations Physics Coach Kelsoe Pages 86–94.
Physics VECTORS AND PROJECTILE MOTION
PHYSICS: Vectors. Today’s Goals Students will: 1.Be able to describe the difference between a vector and a scalar. 2.Be able to draw and add vector’s.
Vectors have magnitude AND direction. – (14m/s west, 32° and falling [brrr!]) Scalars do not have direction, only magnitude. – ( 14m/s, 32° ) Vectors tip.
This lesson will extend your knowledge of kinematics to two dimensions. This lesson will extend your knowledge of kinematics to two dimensions. You will.
Today, we will have a short review on vectors and projectiles and then have a quiz. You will need a calculator, a clicker and some scratch paper for the.
Copyright © Cengage Learning. All rights reserved. Trigonometric Functions: Right Triangle Approach.
CP Vector Components Scalars and Vectors A quantity is something that you measure. Scalar quantities have only size, or amounts. Ex: mass, temperature,
Basics of Trigonometry Click triangle to continue.
The Trigonometric Way Adding Vectors Mathematically.
Resolution and Composition of Vectors. Working with Vectors Mathematically Given a single vector, you may need to break it down into its x and y components.
Do Now: A golf ball is launched at 20 m/s at an angle of 38˚ to the horizontal. 1.What is the vertical component of the velocity? 2.What is the horizontal.
2 Common Ways to Express Vectors Using Magnitude and Direction example d = 5m[ E37°N ] Using Components example d = (4,3) These two examples express the.
VECTOR ADDITION Vectors Vectors Quantities have magnitude and direction and can be represented with; 1. Arrows 2. Sign Conventions (1-Dimension) 3. Angles.
Vectors Chapter 4. Vectors and Scalars What is a vector? –A vector is a quantity that has both magnitude (size, quantity, value, etc.) and direction.
SOHCAHTOA Can only be used for a right triangle
Date: Topic: Trigonometric Ratios (9.5). Sides and Angles x The hypotenuse is always the longest side of the right triangle and is across from the right.
WARM UP Find sin θ, cos θ, tan θ. Then find csc θ, sec θ and cot θ. Find b θ 60° 10 b.
13.1 Right Triangle Trigonometry ©2002 by R. Villar All Rights Reserved.
Vector Basics Characteristics, Properties & Mathematical Functions.
Vectors and Scalars Physics 1 - L.
QQ: Finish Page : Sketch & Label Diagrams for all problems.
Magnitude The magnitude of a vector is represented by its length.
Vectors Vector: a quantity that has both magnitude (size) and direction Examples: displacement, velocity, acceleration Scalar: a quantity that has no.
4.1 Vectors in Physics Objective: Students will know how to resolve 2-Dimensional Vectors from the Magnitude and Direction of a Vector into their Components/Parts.
Physics VECTORS AND PROJECTILE MOTION
Chapter 3.
Physics VECTORS AND PROJECTILE MOTION
Y. Davis Geometry Notes Chapter 8.
Vectors Measured values with a direction
Resolving Vectors in Components
Presentation transcript:

A Demonstrative Approach

Let’s say we need to find the vertical (V Y ) and horizontal (V X ) components of this here vector. The first step is to find the bearing of the vector with respect to a reference point, in this case North, (vertical) or the positive y-axis. 60 o Next, we must find the vertical (v y ) and horizontal (v x ) components by using the trigonometric functions, sine and cosine m sin θ = (opp/hyp) VyVy VxVx sin (60 o ) = (V x /15) Using cross multiplication we get V x = 15.0 * sin (60 o ) = 13.0 m cos θ = (adj/hyp) cos (60 o ) = (V y /15) Using cross multiplication we get V y = 15.0 * cos (60 o ) = 7.50 m Thus, V x = 13.0 m and V y = 7.50 m! North

15.0 m 30 o In this case, the trigonometric functions are switched with respect to the vector components. sin θ = (opp/hyp) cos θ = (adj/hyp)  sin (30 o ) = ( V y / 15.0)  cos (30 o ) = ( V x / 15.0) Notice the trigonometric functions find the opposite component this time. Cross multiplying gives us: V x = 15.0 * cos (30 o ) V y = 15.0 * sin (30 o ) = 13.0 m = 7.50 m Thus, you still have V x = 13.0 m and V y = 7.50 m! As with the ancient art of feng-shui, you must look to the East to find your bearing and thus mark your angle. East VxVx VyVy Whereas in our previous example we had… V x = 15.0 * sin (60º) and V y = 15.0 * cos (60º)

Vectors can have negative quantities if they lie below or to the left of your axes! This vector can have either a negative V x or V y component. Can you explain why? Just keep in mind that the magnitude of the vector stays positive.

Now we will combine vectors by adding them Step One: Take a deep breath, exhale the nervousness, and pray for wisdom. Step Two: This step requires you to determine a reference point to find the bearing for each of your vectors. REMEMBER: Use the smallest angle with reference to one of the four cardinal points: N, S, E, W Step Three: is where you use your angle and trigonometric functions of sin (θ) and cos ( θ) to find your horizontal, v x, and vertical, v y, components to each vector. Step Four: Having found the horizontal, v x, and vertical, v y, components to each vector, you now add all the horizontal components and vertical components separately. 65° 25° 210° 30° 60° V 1 = 18.0m V 2 = 12.0 m v 1x is adjacent to 25° therefore use COS = 18.0 * cos(25°) = 16.3 m v 1y is opposite to 25° therefore use SIN = 18.0 * sin(25°) = 7.61 m Remember the Great Indian Princess… Soh CahToa v 2x is opposite to 30° therefore use SIN… Remember: use since it goes LEFT = * sin(30°) = m v 2y is adjacent to 30° therefore use COS… Remember: use since it goes DOWN = * cos(30°) = m V Rx = 10.3 mV Ry = mV Ry = m …SF Step Five: Draw out your new triangle with the resultant v Rx and v Ry components to determine the length of the resultant. (HINT: Always draw the vector with greatest absolute value first.) Then use the Pythagorean Theorem to find the magnitude of your resultant vector, v R. V R = = 10.7 m Step Six: Having drawn out the new triangle with the resultant v Rx and v Ry components, now you will determine the angle. The direction is given as “θ°lesser of greater” or in this case, as South (lesser vector) of East (greater vector). (Remember Princess SohCahToa!) Use the TAN function to set up your equation, then take the ArcTAN as the inverse function. θ Opp Adj tan (θ) = Vy Vx θ= Atan ( ) θ= 15°South of East