Phys207: Lecture 04. Today s Agenda 3-D Kinematics Independence of x and y components Baseball projectile Shoot the monkey Uniform circular motion
|
|
- Teresa Anthony
- 6 years ago
- Views:
Transcription
1 Phys7: Lecture 4 Reminders All Discussion and Lab sections start meetin this week Homework is posted on course website Solutions to preious hwks will be posted Thursday mornins Today s Aenda 3-D Kinematics Independence of x and y components Baseball projectile Shoot the monkey Uniform circular motion 1 3-D Kinematics The position, elocity, and acceleration of a particle in 3 dimensions can be expressed as: r x i + y j + z k x i + y j + z k (i, j, k unit ectors ) a a x i + a y j + a z k We hae already seen the 1-D kinematics equations: x x(t) dx d d x a Pae 1
2 3-D Kinematics For 3-D, we simply apply the 1-D equations to each of the component equations. x x(t) dx x d x ax y y( t) dy y d y ay z z( t ) dz z d z az Which can be combined into the ector equations: r r(t) dr / a d r / 3 3-D Kinematics So for constant acceleration we can interate to et: a const + a t r r + t + 1 / a t (where a,,, r, r, are all ectors) Link to Actie Fiure Pae
3 -D Kinematics Most 3-D problems can be reduced to -D problems when acceleration is constant: Choose y axis to be alon direction of acceleration Choose x axis to be alon the other direction of motion Example: Throwin a baseball (nelectin air resistance) Acceleration is constant (raity) Choose y axis up: a y - Choose x axis alon the round in the direction of the throw 5 x and y components of motion are independent. A man on a train tosses a ball straiht up in the air. View this from two reference frames: Reference frame on the moin train. Reference frame on the round. 6 Pae 3
4 Problem: Mark McGwire clobbers a fastball toward center-field. The ball is hit 1 m (y o ) aboe the plate, and its initial elocity is 36.5 m/s ( ) at an anle of 3 o (θ) aboe horizontal. The center-field wall is 113 m (D) from the plate and is 3 m (h) hih. What time does the ball reach the fence? Does Mark et a home run? y θ h D 7 Problem... First let s examine the motion Link to Actie Fiure 4-7 Choose y axis up. Choose x axis alon the round in the direction of the hit. Choose the oriin (,) to be at the plate. Say that the ball is hit at t, x x Equations of motion are: x x y y -t x x t y y + y t - 1 / t 8 Pae 4
5 Problem... Use eometry to fiure out x and y : y y θ x y Find x cos θ. and y sin θ. x 9 Problem... The time to reach the wall is: t D / x (easy!) We hae an equation that tell us y(t) y + y t + a t / So, we re done...now we just plu in the numbers: Find: x 36.5 cos(3) m/s 31.6 m/s y 36.5 sin(3) m/s 18.5 m/s t (113 m) / (31.6 m/s) 3.58 s y(t) (1. m) + (18.5 m/s)(3.58 s) - (.5)(9.8 m/s )(3.58 s) ( ) m 3.5 m Since the wall is 3 m hih, Mark ets the homer!! 1 Pae 5
6 Lecture 4, Act 1 Motion in D Two footballs are thrown from the same point on a flat field. Both are thrown at an anle of 3 o aboe the horizontal. Ball has twice the initial speed of ball 1. If ball 1 is cauht a distance D 1 from the thrower, how far away from the thrower D will the receier of ball be when he catches it? (a) D D 1 (b) D 4D 1 (c) D 8D 1 11 Lecture 4, Act 1 Solution The distance a ball will o is simply x (horizontal speed) x (time in air) x t To fiure out time in air, consider the equation for the heiht of the ball: When the ball is cauht, y y y y 1 + y t t 1 t t y t 1 t y two solutions t t y (time of catch) (time of throw) 1 Pae 6
7 x x t Lecture 4, Act 1 Solution So the time spent in the air is proportional to y : t Since the anles are the same, both y and x for ball are twice those of ball 1., y ball 1,1 ball y, y,1 x,1 x, Ball is in the air twice as lon as ball 1, but it also has twice the horizontal speed, so it will o 4 times as far!! 13 Trajectory of projectile (special case of no air resistance) Decompose into x and y motion x x + x t + ½ at ( cosθ)t No horizontal forces y y + y t + ½ at ( sinθ)t ½ t Eliminate t usin t x / ( cosθ) y x x cos θ ( tanθ ) Trajectory is a parabola Specified by only initial speed and launch anle 14 Pae 7
8 Maximum heiht of projectile (special case of symmetric trajectory) At peak y, so y y -t A sinθ t sinθ ta A h max + y t A ½ t A ( sinθ ) sinθ 1 sinθ sin θ 15 Horizontal rane of projectile (special case of symmetric trajectory) Total time in air is t A Rane R x total time in air ( θ ) R cos t A sinθ ( cosθ ) sin θ (recall sinθ sinθ cosθ ) Rmax at θ 45 Let s examine some trajectories Link to Actie Fiure Pae 8
9 Shootin the Monkey (tranquilizer un) Where does the zookeeper aim if he wants to hit the monkey? ( He knows the monkey will let o as soon as he shoots! ) 17 Shootin the Monkey... If there were no raity, simply aim at the monkey r r r t 18 Pae 9
10 Shootin the Monkey... With raity, still aim at the monkey! r r - 1 / t r t - 1 / t Dart hits the monkey! 19 Recap: Shootin the monkey... x t y - 1 / t This may be easier to think about. It s exactly the same idea!! x x y - 1 / t Pae 1
Get Solution of These Packages & Learn by Video Tutorials on PROJECTILE MOTION
FREE Download Study Packae from website: www.tekoclasses.com & www.mathsbysuha.com Get Solution of These Packaes & Learn by Video Tutorials on www.mathsbysuha.com. BASIC CONCEPT :. PROJECTILE PROJECTILE
More informationPhysics 111. Lecture 7 (Walker: 4.2-5) 2D Motion Examples Projectile Motion
Physics 111 Lecture 7 (Walker: 4.-5) D Motion Eamples Projectile Motion Sept. 16, 9 -D Motion -- Constant Acceleration r r r r = v t at t v t a t y y yt y v t at r r r v = v at v = v a t v = v a t y y
More informationMotion in Two or Three Dimensions
Chapter 3 Motion in Two or Three Dimensions PowerPoint Lectures for University Physics, Thirteenth Edition Hugh D. Young and Roger A. Freedman Lectures by Wayne Anderson Goals for Chapter 3 To use vectors
More informationRutgers University Department of Physics & Astronomy. 01:750:271 Honors Physics I Fall Lecture 4. Home Page. Title Page. Page 1 of 35.
Rutgers Uniersit Department of Phsics & Astronom 01:750:271 Honors Phsics I Fall 2015 Lecture 4 Page 1 of 35 4. Motion in two and three dimensions Goals: To stud position, elocit, and acceleration ectors
More informationPHYS 100: Lecture 4 PROJECTILE MOTION. y = (v 0 /v T ) x (g/2v T2 )x 2. Velocity of Train v T. Physics 100 Lecture 4, Slide y(m)
PHYS : Lecture 4 PROJECTILE MOTION.4. Velocity of Train T y(m).8.6.4. 5 5 x(m) y ( / T ) x (/ T )x Physics Lecture 4, Slide Music Who is the Artist? A) Miles Dais B) Wynton Marsalis C) Chris Botti D) Nina
More informationREVIEW: Going from ONE to TWO Dimensions with Kinematics. Review of one dimension, constant acceleration kinematics. v x (t) = v x0 + a x t
Lecture 5: Projectile motion, uniform circular motion 1 REVIEW: Goin from ONE to TWO Dimensions with Kinematics In Lecture 2, we studied the motion of a particle in just one dimension. The concepts of
More informationv( t) g 2 v 0 sin θ ( ) ( ) g t ( ) = 0
PROJECTILE MOTION Velocity We seek to explore the velocity of the projectile, includin its final value as it hits the round, or a taret above the round. The anle made by the velocity vector with the local
More informationjfpr% ekuo /kez iz.ksrk ln~xq# Jh j.knksm+nklth egkjkt
Phone : 0 903 903 7779, 98930 58881 Kinematics Pae: 1 fo/u fopkjr Hkh# tu] uha kjehks dke] foifr ns[k NksM+s rqjar e/;e eu dj ';kea iq#"k fla ladyi dj] lrs foifr usd] ^cuk^ u NksM+s /;s; dks] j?kqcj jk[ks
More information3.2 Projectile Motion
Motion in 2-D: Last class we were analyzing the distance in two-dimensional motion and revisited the concept of vectors, and unit-vector notation. We had our receiver run up the field then slant Northwest.
More informationLecture 02: 2D Kinematics. Physics 2210 Fall Semester 2014
Lecture 02: 2D Kinematics Physics 2210 Fall Semester 2014 Announcements Note that all Prelectures, Checkpoint Quizzes, and Homeworks are available one week before due date. You should have done Prelecture
More informationProblem Set: Fall #1 - Solutions
Problem Set: Fall #1 - Solutions 1. (a) The car stops speedin up in the neative direction and beins deceleratin, probably brakin. (b) Calculate the averae velocity over each time interval. v av0 v 0 +
More informationLinear Motion. Miroslav Mihaylov. February 13, 2014
Linear Motion Miroslav Mihaylov February 13, 2014 1 Vector components Vector A has manitude A and direction θ with respect to the horizontal. On Fiure 1 we chose the eastbound as a positive x direction
More informationKINEMATICS PREVIOUS EAMCET BITS ENGINEERING PAPER
KINEMATICS PREVIOUS EAMCET BITS ENGINEERING PAPER. A body is projected vertically upwards at time t = 0 and is seen at a heiht at time t and t seconds durin its fliht. The maximum heiht attained is [ =
More informationChapter 2. Kinematics in One Dimension. continued
Chapter 2 Kinematics in One Dimension continued 2.6 Freely Falling Bodies Example 10 A Falling Stone A stone is dropped from the top of a tall building. After 3.00s of free fall, what is the displacement
More informationFeb 6, 2013 PHYSICS I Lecture 5
95.141 Feb 6, 213 PHYSICS I Lecture 5 Course website: faculty.uml.edu/pchowdhury/95.141/ www.masteringphysics.com Course: UML95141SPRING213 Lecture Capture h"p://echo36.uml.edu/chowdhury213/physics1spring.html
More informationThere seems to be three different groups of students: A group around 6 A group around 12 A group around 16
10 5 0 0 5 10 15 20 25 30 There seems to be three different groups of students: A group around 6 A group around 12 A group around 16 Altuğ Özpineci ( METU ) Phys109-MECHANICS PHYS109 55 / 67 10 5 0 0 5
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 informationMotion in Two Dimensions Sections Covered in the Text: Chapters 6 & 7, except 7.5 & 7.6
Motion in Two Dimensions Sections Covered in the Tet: Chapters 6 & 7, ecept 7.5 & 7.6 It is time to etend the definitions we developed in Note 03 to describe motion in 2D space. In doin so we shall find
More informationXI PHYSICS M. AFFAN KHAN LECTURER PHYSICS, AKHSS, K. https://promotephysics.wordpress.com
XI PHYSICS M. AFFAN KHAN LECTURER PHYSICS, AKHSS, K affan_414@live.com https://promotephysics.wordpress.com [MOTION IN TWO DIMENSIONS] CHAPTER NO. 4 In this chapter we are oin to discuss motion in projectile
More information2.5 Velocity and Acceleration
82 CHAPTER 2. VECTOR FUNCTIONS 2.5 Velocity and Acceleration In this section, we study the motion of an object alon a space curve. In other words, as the object moves with time, its trajectory follows
More informationDynamics 4600:203 Homework 03 Due: February 08, 2008 Name:
Dynamics 4600:03 Homework 03 Due: ebruary 08, 008 Name: Please denote your answers clearly, i.e., bo in, star, etc., and write neatly. There are no points for small, messy, unreadable work... please use
More informationPHYS 1114, Lecture 9, February 6 Contents:
PHYS 4, Lecture 9, February 6 Contents: Continued with projectile motion: The kicko problem in football was treated analytically, obtainin formulas for maimum heiht and rane in terms of initial speed and
More informationVectors and Scalars. Scalar: A quantity specified by its magnitude only Vector: A quantity specified both by its magnitude and direction.
Vectors and Scalars Scalar: A quantity specified by its magnitude only Vector: A quantity specified both by its magnitude and direction. To distinguish a vector from a scalar quantity, it is usually written
More informationChapter 4 Two-Dimensional Kinematics. Copyright 2010 Pearson Education, Inc.
Chapter 4 Two-Dimensional Kinematics Units of Chapter 4 Motion in Two Dimensions Projectile Motion: Basic Equations Zero Launch Angle General Launch Angle Projectile Motion: Key Characteristics 4-1 Motion
More informationTwo-Dimensional Motion Worksheet
Name Pd Date Two-Dimensional Motion Worksheet Because perpendicular vectors are independent of each other we can use the kinematic equations to analyze the vertical (y) and horizontal (x) components of
More informationEnergizing Math with Engineering Applications
Enerizin Math with Enineerin Applications Understandin the Math behind Launchin a Straw-Rocket throuh the use of Simulations. Activity created by Ira Rosenthal (rosenthi@palmbeachstate.edu) as part of
More informationPhysics 111. Lecture 8 (Walker: 4.3-5) 2D Motion Examples. Projectile - General Launch Angle. In general, v 0x = v 0 cos θ and v 0y = v 0 sin θ
Physics 111 Lecture 8 (Walker: 4.3-5) D Motion Examples February 13, 009 Lecture 8 1/ Projectile - General Launch Angle In general, v 0x = v 0 cos θ and v 0y = v 0 sin θ (This ASSUMES θ is measured CCW
More informationPHY 1114: Physics I. Quick Question 1. Quick Question 2. Quick Question 3. Quick Question 4. Lecture 5: Motion in 2D
PHY 1114: Physics I Lecture 5: Motion in D Fall 01 Kenny L. Tapp Quick Question 1 A child throws a ball vertically upward at the school playground. Which one of the following quantities is (are) equal
More informationClassical Mechanics Lecture 2
Classical Mechanics Lecture 2 Today's Concepts: a) Vectors b) Projec@le mo@on c) Reference frames Mechanics Lecture 2, Slide 1 Unit 6 Activity Guide Today Name Date (YY/MM/DD) / / SFU e-mail @sfu.ca Section
More informationPhysics 1: Mechanics
Physics 1: Mechanics Đào Ngọc Hạnh Tâm Office: A1.53, Email: dnhtam@hcmiu.edu.n HCMIU, Vietnam National Uniersity Acknowledgment: Most of these slides are supported by Prof. Phan Bao Ngoc credits (3 teaching
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 information2-D Kinematics. In general, we have the following 8 equations (4 per dimension): Notes Page 1 of 7
2-D Kinematics The problem we run into with 1-D kinematics, is that well it s one dimensional. We will now study kinematics in two dimensions. Obviously the real world happens in three dimensions, but
More informationphysics Chapter 4 Lecture a strategic approach randall d. knight FOR SCIENTISTS AND ENGINEERS Chapter 4_Lecture1 THIRD EDITION
Chapter 4 Lecture physics FOR SCIENTISTS AND ENGINEERS a strategic approach THIRD EDITION randall d. knight Chapter 4_Lecture1 1 Chapter 4 Kinematics in 2D: Projectile Motion (Sec. 4.2) Which fountain
More informationStatus: Unit 2, Chapter 3
1 Status: Unit, Chapter 3 Vectors and Scalars Addition of Vectors Graphical Methods Subtraction of Vectors, and Multiplication by a Scalar Adding Vectors by Components Unit Vectors Vector Kinematics Projectile
More informationThe centripetal acceleration for a particle moving in a circle is a c = v 2 /r, where v is its speed and r is its instantaneous radius of rotation.
skiladæmi 1 Due: 11:59pm on Wednesday, September 9, 2015 You will receive no credit for items you complete after the assignment is due. Grading Policy Problem 3.04 The horizontal coordinates of a in a
More information2.2 Differentiation and Integration of Vector-Valued Functions
.. DIFFERENTIATION AND INTEGRATION OF VECTOR-VALUED FUNCTIONS133. Differentiation and Interation of Vector-Valued Functions Simply put, we differentiate and interate vector functions by differentiatin
More informationWelcome back to Physics 211
Welcome back to Physics 211 The room is very full please move toward the center and help others find a seat. Be patient. The registration database is only updated twice per week. Get to know the people
More informationINTRODUCTION. 3. Two-Dimensional Kinematics
INTRODUCTION We now extend our study of kinematics to motion in two dimensions (x and y axes) This will help in the study of such phenomena as projectile motion Projectile motion is the study of objects
More informationPhysics 4A Solutions to Chapter 4 Homework
Physics 4A Solutions to Chapter 4 Homework Chapter 4 Questions: 4, 1, 1 Exercises & Problems: 5, 11, 3, 7, 8, 58, 67, 77, 87, 11 Answers to Questions: Q 4-4 (a) all tie (b) 1 and tie (the rocket is shot
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 informationUNDERSTAND MOTION IN ONE AND TWO DIMENSIONS
SUBAREA I. COMPETENCY 1.0 UNDERSTAND MOTION IN ONE AND TWO DIMENSIONS MECHANICS Skill 1.1 Calculating displacement, aerage elocity, instantaneous elocity, and acceleration in a gien frame of reference
More informationAnnouncements. Unit 1 homework due tomorrow 11:59 PM Quiz 1 on 3:00P Unit 1. Units 2 & 3 homework sets due 11:59 PM
Announcements Unit 1 homework due tomorrow (Tuesday) @ 11:59 PM Quiz 1 on Wednesday @ 3:00P Unit 1 Ø First 12 minutes of class: be on time!!! Units 2 & 3 homework sets due Sunday @ 11:59 PM Ø Most homework
More informationFebruary 8, Week 4. Today: Chapter 3, Projectile Motion. Homework #1 now in boxes.
February 8, Week 4 Today: Chapter 3, Projectile Motion Homework #1 now in boxes. No New homework assignment this week. Homework Solutions posted Thursday morning. Chapter 2 practice problems on Mastering
More informationMotion in Two and Three Dimensions
PH 1-1D Spring 013 Motion in Two and Three Dimensions Lectures 5,6,7 Chapter 4 (Halliday/Resnick/Walker, Fundamentals of Physics 9 th edition) 1 Chapter 4 Motion in Two and Three Dimensions In this chapter
More informationProjectile Motion. v a = -9.8 m/s 2. Good practice problems in book: 3.23, 3.25, 3.27, 3.29, 3.31, 3.33, 3.43, 3.47, 3.51, 3.53, 3.
v a = -9.8 m/s 2 A projectile is anything experiencing free-fall, particularly in two dimensions. 3.23, 3.25, 3.27, 3.29, 3.31, 3.33, 3.43, 3.47, 3.51, 3.53, 3.55 Projectile Motion Good practice problems
More information2. Two Dimensional Kinematics
. Two Dimensional Kinematics A) Overview We will begin by introducing the concept of vectors that will allow us to generalize what we learned last time in one dimension to two and three dimensions. In
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 informationIntroduction to 2-Dimensional Motion
Introduction to 2-Dimensional Motion 2-Dimensional Motion! Definition: motion that occurs with both x and y components.! Example:! Playing pool.! Throwing a ball to another person.! Each dimension of the
More informationGround Rules. PC1221 Fundamentals of Physics I. Position and Displacement. Average Velocity. Lectures 7 and 8 Motion in Two Dimensions
PC11 Fundamentals of Physics I Lectures 7 and 8 Motion in Two Dimensions Dr Tay Sen Chuan 1 Ground Rules Switch off your handphone and paer Switch off your laptop computer and keep it No talkin while lecture
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 informationClassical Mechanics Lecture 2
Classical Mechanics Lecture 2 Today's Concepts: a) Vectors b) Projec@le mo@on c) Reference frames Mechanics Lecture 2, Slide 1 Unit 6 Activity Guide Today Not everyone is doing the pre-lecture This is
More informationFiring an Ideal Projectile
92 Chapter 13: Vector-Valued Functions and Motion in Space 13.2 Modelin Projectile Motion 921 r at time t v v cos i a j (a) v sin j Newton s second law of motion sas that the force actin on the projectile
More information(a) 1m s -2 (b) 2 m s -2 (c) zero (d) -1 m s -2
11 th Physics - Unit 2 Kinematics Solutions for the Textbook Problems One Marks 1. Which one of the followin Cartesian coordinate system is not followed in physics? 5. If a particle has neative velocity
More informationPhysics Kinematics: Projectile Motion. Science and Mathematics Education Research Group
F FA ACULTY C U L T Y OF O F EDUCATION E D U C A T I O N Department of Curriculum and Pedagogy Physics Kinematics: Projectile Motion Science and Mathematics Education Research Group Supported by UBC Teaching
More informationProjectile Motion. Equipment: Ballistic Gun Apparatus Projectiles Table Clamps 2-meter Stick Carbon Paper, Scratch Paper, Masking Tape Plumb Bob
Purpose: To calculate the initial speed of a projectile by measurin its rane. To predict how far a projectile will travel when fired at different anles, and test these predictions. To predict what anle
More informationBell Ringer. x- direction: Ball and car start with same position and velocity, a=0, so always have same position
Objectives Students should be able to add, subtract, and resolve displacement and velocity vectors so they can: Determine the components of a vector along two specified, mutually perpendicular axes. Determine
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 informationthe equations for the motion of the particle are written as
Dynamics 4600:203 Homework 02 Due: ebruary 01, 2008 Name: Please denote your answers clearly, ie, box in, star, etc, and write neatly There are no points for small, messy, unreadable work please use lots
More informationPhysics 121. Tuesday, January 29, 2008.
Physics 121. Tuesday, January 29, 2008. This is where your instructor grew up. Schiphol (Amsterdam Airport) = cemetery of ships. Physics 121. Tuesday, January 29, 2008. Topics: Course announcements Quiz
More informationThis Week. Next Week
This Week Tutorial and Test 1, in the lab (chapters 1 and 2) Next Week Experiment 1: Measurement of Lenth and Mass WileyPLUS Assinment 1 now available Due Monday, October 5 at 11:00 pm Chapters 2 & 3 28
More informationTopic 1: 2D Motion PHYSICS 231
Topic 1: 2D Motion PHYSICS 231 Current Assignments Homework Set 1 due this Thursday, Jan 20, 11 pm Homework Set 2 due Thursday, Jan 27, 11pm Reading: Chapter 4,5 for next week 2/1/11 Physics 231 Spring
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 informationPhysics 1A. Lecture 3B. "More than anything else... any guy here would love to have a monkey. A pet monkey." -- Dane Cook
Physics 1A Lecture 3B "More than anything else... any guy here would love to have a monkey. A pet monkey." -- Dane Cook Trajectories Since there is no horizontal acceleration (a x = 0) the horizontal position,
More informationWhen we throw a ball :
PROJECTILE MOTION When we throw a ball : There is a constant velocity horizontal motion And there is an accelerated vertical motion These components act independently of each other PROJECTILE MOTION A
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 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 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 informationISSUED BY K V - DOWNLOADED FROM KINEMATICS
KINEMATICS *rest and Motion are relative terms, nobody can exist in a state of absolute rest or of absolute motion. *One dimensional motion:- The motion of an object is said to be one dimensional motion
More informationKINEMATICS OF PARTICLES PROBLEMS ON RELATIVE MOTION WITH RESPECT TO TRANSLATING AXES
KINEMATICS OF PARTICLES PROBLEMS ON RELATIVE MOTION WITH RESPECT TO TRANSLATING AXES 1. The car A has a forward speed of 18 km/h and is accelerating at 3 m/s2. Determine the elocity and acceleration of
More informationPSI AP Physics C Kinematics 2D. Multiple Choice Questions
PSI AP Physics C Kinematics D Multiple Choice Questions 1. A tennis ball is thrown off a cliff 10 m above the round with an initial horizontal velocity of 5 m/s as shown above. The time between the ball
More informationCHAPTER 3 MOTION IN TWO AND THREE DIMENSIONS
CHAPTER 3 MOTION IN TWO AND THREE DIMENSIONS General properties of vectors displacement vector position and velocity vectors acceleration vector equations of motion in 2- and 3-dimensions Projectile motion
More informationCircular motion. Announcements:
Circular motion Announcements: Clicker scores through Wednesday are now posted on DL. Scoring is points for a wrong answer, 3 points for a right answer. 13 clicker questions so far, so max is 39 points.
More informationPhysics 11 Fall 2012 Practice Problems 2 - Solutions
Physics 11 Fall 01 Practice Problems - s 1. True or false (inore any effects due to air resistance): (a) When a projectile is fired horizontally, it takes the same amount of time to reach the round as
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 informationParametric Equations
Parametric Equations Suppose a cricket jumps off of the round with an initial velocity v 0 at an anle θ. If we take his initial position as the oriin, his horizontal and vertical positions follow the equations:
More information1 CHAPTER 7 PROJECTILES. 7.1 No Air Resistance
CHAPTER 7 PROJECTILES 7 No Air Resistance We suppose that a particle is projected from a point O at the oriin of a coordinate system, the y-axis bein vertical and the x-axis directed alon the round The
More informationChapter 3: Vectors and Projectile Motion
Chapter 3: Vectors and Projectile Motion Vectors and Scalars You might remember from math class the term vector. We define a vector as something with both magnitude and direction. For example, 15 meters/second
More informationDemo: x-t, v-t and a-t of a falling basket ball.
Demo: x-t, v-t and a-t of a falling basket ball. I-clicker question 3-1: A particle moves with the position-versus-time graph shown. Which graph best illustrates the velocity of the particle as a function
More information(a) Taking the derivative of the position vector with respect to time, we have, in SI units (m/s),
Chapter 4 Student Solutions Manual. We apply Eq. 4- and Eq. 4-6. (a) Taking the deriatie of the position ector with respect to time, we hae, in SI units (m/s), d ˆ = (i + 4t ˆj + tk) ˆ = 8tˆj + k ˆ. dt
More informationProjectile Motion. Practice test Reminder: test Feb 8, 7-10pm! me if you have conflicts! Your intuitive understanding of the Physical world
v a = -9.8 m/s Projectile Motion Good practice problems in book: 3.3, 3.5, 3.7, 3.9, 3.31, 3.33, 3.43, 3.47, 3.51, 3.53, 3.55 Practice test Reminder: test Feb 8, 7-10pm! Email me if you have conflicts!
More informationProblem Set 2 Solutions
UNIVERSITY OF ALABAMA Department of Physics and Astronomy PH 125 / LeClair Sprin 2009 Problem Set 2 Solutions The followin three problems are due 20 January 2009 at the beinnin of class. 1. (H,R,&W 4.39)
More informationBell Ringer: What is constant acceleration? What is projectile motion?
Bell Ringer: What is constant acceleration? What is projectile motion? Can we analyze the motion of an object on the y-axis independently of the object s motion on the x-axis? NOTES 3.2: 2D Motion: Projectile
More informationProjectile Motion. Chin- Sung Lin STEM GARAGE SCIENCE PHYSICS
Projectile Motion Chin- Sung Lin Introduction to Projectile Motion q What is Projectile Motion? q Trajectory of a Projectile q Calculation of Projectile Motion Introduction to Projectile Motion q What
More informationYour Thoughts. What is the difference between elastic collision and inelastic collision?
Your Thoughts This seemed pretty easy...before we got the checkpoint questions What is the difference between elastic collision and inelastic collision? The most confusing part of the pre lecture was the
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 informationPROJECTILE MOTION. ( ) g y 0. Equations ( ) General time of flight (TOF) General range. Angle for maximum range ("optimum angle")
PROJECTILE MOTION Equations General time of fliht (TOF) T sin θ y 0 sin( θ) General rane R cos( θ) T R cos θ sin( θ) sin( θ) y 0 Anle for maximum rane ("optimum anle") θ opt atan y 0 atan v f atan v f
More informationPhys 2425: University Physics I Spring 2016 Practice Exam 1
1. (0 Points) What course is this? a. PHYS 1401 b. PHYS 140 c. PHYS 45 d. PHYS 46 Survey Questions no points. (0 Points) Which exam is this? a. Exam 1 b. Exam c. Final Exam 3. (0 Points) What version of
More informationPhysics 2A Chapter 3 - Motion in Two Dimensions Fall 2017
These notes are seen pages. A quick summary: Projectile motion is simply horizontal motion at constant elocity with ertical motion at constant acceleration. An object moing in a circular path experiences
More informationChapter 1: Kinematics of Particles
Chapter 1: Kinematics of Particles 1.1 INTRODUCTION Mechanics the state of rest of motion of bodies subjected to the action of forces Static equilibrium of a body that is either at rest or moes with constant
More informationPhysics 111. Lecture 8 (Walker: 5.1-3) Force (F) Mass (m) Newton s 2 nd Law: F = ma. Summary - 2D Kinematics. = (20.0 m/s)(6.
Physics Lecture 8 (Walker: 5.-3) Force (F) Mass (m) Newton s nd Law: F = ma Example: A Supply Drop Helicopter drops supply package to flood victims on raft. When package is released, helicopter is 00 m
More informationChapter 3: Kinematics in Two Dimensions
Chapter 3: Kinematics in Two Dimensions Vectors and Scalars A scalar is a number with units. It can be positive, negative, or zero. Time: 100 s Distance and speed are scalars, although they cannot be negative
More informationUniversity of Alabama Department of Physics and Astronomy. PH 105 LeClair Summer Problem Set 3 Solutions
University of Alabama Department of Physics and Astronomy PH 105 LeClair Summer 2012 Instructions: Problem Set 3 Solutions 1. Answer all questions below. All questions have equal weight. 2. Show your work
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 informationIn this activity, we explore the application of differential equations to the real world as applied to projectile motion.
Applications of Calculus: Projectile Motion ID: XXXX Name Class In this activity, we explore the application of differential equations to the real world as applied to projectile motion. Open the file CalcActXX_Projectile_Motion_EN.tns
More informationGeodesics as gravity
Geodesics as ravity February 8, 05 It is not obvious that curvature can account for ravity. The orbitin path of a planet, for example, does not immediately seem to be the shortest path between points.
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 informationMOTION OF A PROJECTILE
MOTION OF A PROJECTILE Today s Objectives: Students will be able to: 1. Analyze the free-flight motion of a projectile. In-Class Activities: Check Homework Reading Quiz Applications Kinematic Equations
More informationAP Physics First Nine Weeks Review
AP Physics First Nine Weeks Review 1. If F1 is the magnitude of the force exerted by the Earth on a satellite in orbit about the Earth and F2 is the magnitude of the force exerted by the satellite on the
More information3 Vectors and Two- Dimensional Motion
May 25, 1998 3 Vectors and Two- Dimensional Motion Kinematics of a Particle Moving in a Plane Motion in two dimensions is easily comprehended if one thinks of the motion as being made up of two independent
More informationPS 11 GeneralPhysics I for the Life Sciences
PS 11 GeneralPhysics I for the Life Sciences M E C H A N I C S I D R. B E N J A M I N C H A N A S S O C I A T E P R O F E S S O R P H Y S I C S D E P A R T M E N T N O V E M B E R 0 1 3 Definition Mechanics
More information