1. Six acceleration vectors are shown for the car whose velocity vector is directed forward. For each acceleration vector describe in words the

Size: px
Start display at page:

Download "1. Six acceleration vectors are shown for the car whose velocity vector is directed forward. For each acceleration vector describe in words the"

Transcription

1 Si ccelerio ecors re show for he cr whose eloci ecor is direced forwrd For ech ccelerio ecor describe i words he iseous moio of he cr

2 A ri eers cured horizol secio of rck speed of 00 km/h d slows dow wih cos decelerio o 50 km/h i secods A cceleromeer moued iside he ri records horizol ccelerio of m/s whe he ri is 6 secods io he cure Clcule he rdius of curure r of he rck for his is whe =6 s, r=? 50 km/h = s m/s =6 s 00 km/h =0 57 m / s 6 6 o o m / s km/ h m / s r r m

3 3 The desig of cmshf-drie ssem of four-clider uomobile egie is show As he egie is reed up, he bel speed chges uiforml from 3 m/s o 6 m/s oer wo-secod ierl Clcule he mgiudes of he ccelerios of pois d hlfw hrough his ime ierl

4 : circulr moio : recilier moio s m / s m / s m / s m / o o Clcule he mgiudes of he ccelerios of pois d hlfw hrough his ime ierl (eloci hlfw hrough his ime ierl = s)

5 4 A smll pricle srs from poi O wih egligible speed d icreses is speed o lue = gh, where is he ericl drop from O Whe =5 m, deermie he -compoe of ccelerio of he pricle m m, 0 008? 8 m r r d d d d 3 / 5 3 / d d m 0 06 d d 0 5 m / s r 0 4, 5 94 m / s d 0 06 d

6 5 A pricle rels log he ph =4 wih cos speed of =4 m/s Deermie he d compoes of he pricle s eloci d ccelerio whe he pricle is =4 m

7 6 A foobll pler releses bll wih he iiil codiios show i he figure Neglec mospheric resisce d chge i g d compue he rdius of curure r of he ph of he bll d he ime re of chge of he speed () jus fer relese, (b) he pe, d (c) ime = s o =30 m/s 30 o

8 7 The pi is cosried o moe i he sloed guides which moe righ gles o oe oher A he is represeed, A hs eloci o he righ of 0 m/s which is decresig he re of 075 m/s ech secod A he sme ime, is moig dow wih eloci of 05 m/s which is decresig he re of 05 m/s ech secod For his is, deermie he rdius of curure r of he ph followed b

9 8 A bll is hrow horizoll from he op of 50 m cliff A wih speed of 5 m/s d lds poi C ecuse of srog horizol wid he bll hs cos ccelerio i he egie -direcio Deermie he rdius of curure r of he ph of he bll where is rjecor mkes gle of 45 o wih he horizol Neglec effec of ir resisce i he ericl direcio

10 5 m s A A / ge o he rjecor oi C Horizol: C A A C C Vericl: C A A g C C m / s s oi A 5 54 A g o s 3 97 m / s 834 m / s =98 m/s =54 m/s m / s 98 si si m / s 834 r 4 9 r 804 m

11 9 I he desig of corol mechism, he ericl sloed guide is moig wih cos eloci =50 mm/s durig he ierl of is moio from =80 mm o =+80 mm For he is whe = 60 mm, clcule he - d -compoes of ccelerio of he pi, which is cofied o moe i he prbolic grooe From hese resuls, deermie he rdius of curure r of he ph his posiio

12 whe = 60 mm, clcule he - d -compoes of ccelerio of he pi, he rdius of curure r of he ph Equio of rjecor: = + b =0 =00 mm 00=+b(0 ) =00 =00 =0 0=00+b(00 ) b=/ mm / s ( cs) mm / s 50i 80 j e Veloci Vecor i Cresi Coordies mm / s Mgiude of Veloci Veloci Vecor i Norml &Tgeil Coordies

13 Accelerio + d d mm / s ( cs) o mm / s 50i 509 o 34307e 80 j 0 r 450cos i 80 j 34307e 450 j 8809 mm / s 450si mm / s mm // 450 j // d d d d r d d 3/ 3/ 906 mm 50 d d 50

One of the common descriptions of curvilinear motion uses path variables, which are measurements made along the tangent t and normal n to the path of

One of the common descriptions of curvilinear motion uses path variables, which are measurements made along the tangent t and normal n to the path of Oe of he commo descipios of cuilie moio uses ph ibles, which e mesuemes mde log he ge d oml o he ph of he picles. d e wo ohogol xes cosideed sepely fo eey is of moio. These coodies poide ul descipio fo

More information

Physics 101 Lecture 4 Motion in 2D and 3D

Physics 101 Lecture 4 Motion in 2D and 3D Phsics 11 Lecure 4 Moion in D nd 3D Dr. Ali ÖVGÜN EMU Phsics Deprmen www.ogun.com Vecor nd is componens The componens re he legs of he righ ringle whose hpoenuse is A A A A A n ( θ ) A Acos( θ) A A A nd

More information

TEST-12 TOPIC : SHM and WAVES

TEST-12 TOPIC : SHM and WAVES Q. Four sprig coec wih ss s show i figure. Fid frequecy of S.H.. TEST- TOPIC : SH d WVES 4 7 (D) These wo coeced i series. So = = Now ll re i prllel so eq = 4 so freq. = 4 4 7 Q. sll ss execue S.H.. bou

More information

PHY2048 Exam 1 Formula Sheet Vectors. Motion. v ave (3 dim) ( (1 dim) dt. ( (3 dim) Equations of Motion (Constant Acceleration)

PHY2048 Exam 1 Formula Sheet Vectors. Motion. v ave (3 dim) ( (1 dim) dt. ( (3 dim) Equations of Motion (Constant Acceleration) Insrucors: Field/Mche PHYSICS DEPATMENT PHY 48 Em Ferur, 5 Nme prin, ls firs: Signure: On m honor, I he neiher gien nor receied unuhoried id on his eminion. YOU TEST NUMBE IS THE 5-DIGIT NUMBE AT THE TOP

More information

when t = 2 s. Sketch the path for the first 2 seconds of motion and show the velocity and acceleration vectors for t = 2 s.(2/63)

when t = 2 s. Sketch the path for the first 2 seconds of motion and show the velocity and acceleration vectors for t = 2 s.(2/63) . The -coordine of pricle in curiliner oion i gien b where i in eer nd i in econd. The -coponen of ccelerion in eer per econd ured i gien b =. If he pricle h -coponen = nd when = find he gniude of he eloci

More information

Physic 231 Lecture 4. Mi it ftd l t. Main points of today s lecture: Example: addition of velocities Trajectories of objects in 2 = =

Physic 231 Lecture 4. Mi it ftd l t. Main points of today s lecture: Example: addition of velocities Trajectories of objects in 2 = = Mi i fd l Phsic 3 Lecure 4 Min poins of od s lecure: Emple: ddiion of elociies Trjecories of objecs in dimensions: dimensions: g 9.8m/s downwrds ( ) g o g g Emple: A foobll pler runs he pern gien in he

More information

A 1.3 m 2.5 m 2.8 m. x = m m = 8400 m. y = 4900 m 3200 m = 1700 m

A 1.3 m 2.5 m 2.8 m. x = m m = 8400 m. y = 4900 m 3200 m = 1700 m PHYS : Soluions o Chper 3 Home Work. SSM REASONING The displcemen is ecor drwn from he iniil posiion o he finl posiion. The mgniude of he displcemen is he shores disnce beween he posiions. Noe h i is onl

More information

1. Consider a PSA initially at rest in the beginning of the left-hand end of a long ISS corridor. Assume xo = 0 on the left end of the ISS corridor.

1. Consider a PSA initially at rest in the beginning of the left-hand end of a long ISS corridor. Assume xo = 0 on the left end of the ISS corridor. In Eercise 1, use sndrd recngulr Cresin coordine sysem. Le ime be represened long he horizonl is. Assume ll ccelerions nd decelerions re consn. 1. Consider PSA iniilly res in he beginning of he lef-hnd

More information

F.Y. Diploma : Sem. II [CE/CR/CS] Applied Mathematics

F.Y. Diploma : Sem. II [CE/CR/CS] Applied Mathematics F.Y. Diplom : Sem. II [CE/CR/CS] Applied Mhemics Prelim Quesio Pper Soluio Q. Aemp y FIVE of he followig : [0] Q. () Defie Eve d odd fucios. [] As.: A fucio f() is sid o e eve fucio if f() f() A fucio

More information

Week 8 Lecture 3: Problems 49, 50 Fourier analysis Courseware pp (don t look at French very confusing look in the Courseware instead)

Week 8 Lecture 3: Problems 49, 50 Fourier analysis Courseware pp (don t look at French very confusing look in the Courseware instead) Week 8 Lecure 3: Problems 49, 5 Fourier lysis Coursewre pp 6-7 (do look Frech very cofusig look i he Coursewre ised) Fourier lysis ivolves ddig wves d heir hrmoics, so i would hve urlly followed fer he

More information

Motion in a Straight Line

Motion in a Straight Line Moion in Srigh Line. Preei reched he mero sion nd found h he esclor ws no working. She wlked up he sionry esclor in ime. On oher dys, if she remins sionry on he moing esclor, hen he esclor kes her up in

More information

Physics 232 Exam I Feb. 13, 2006

Physics 232 Exam I Feb. 13, 2006 Phsics I Fe. 6 oc. ec # Ne..5 g ss is ched o hoizol spig d is eecuig siple hoic oio. The oio hs peiod o.59 secods. iiil ie i is oud o e 8.66 c o he igh o he equiliiu posiio d oig o he le wih eloci o sec.

More information

2D Motion WS. A horizontally launched projectile s initial vertical velocity is zero. Solve the following problems with this information.

2D Motion WS. A horizontally launched projectile s initial vertical velocity is zero. Solve the following problems with this information. Nme D Moion WS The equions of moion h rele o projeciles were discussed in he Projecile Moion Anlsis Acii. ou found h projecile moes wih consn eloci in he horizonl direcion nd consn ccelerion in he ericl

More information

Physics 2A HW #3 Solutions

Physics 2A HW #3 Solutions Chper 3 Focus on Conceps: 3, 4, 6, 9 Problems: 9, 9, 3, 41, 66, 7, 75, 77 Phsics A HW #3 Soluions Focus On Conceps 3-3 (c) The ccelerion due o grvi is he sme for boh blls, despie he fc h he hve differen

More information

Physics 232 Exam I Feb. 14, 2005

Physics 232 Exam I Feb. 14, 2005 Phsics I Fe., 5 oc. ec # Ne..5 g ss is ched o hoizol spig d is eecuig siple hoic oio wih gul eloci o dissec. gie is i ie i is oud o e 8 c o he igh o he equiliiu posiio d oig o he le wih eloci o.5 sec..

More information

Fresnel Dragging Explained

Fresnel Dragging Explained Fresel Draggig Explaied 07/05/008 Decla Traill Decla@espace.e.au The Fresel Draggig Coefficie required o explai he resul of he Fizeau experime ca be easily explaied by usig he priciples of Eergy Field

More information

3 Motion with constant acceleration: Linear and projectile motion

3 Motion with constant acceleration: Linear and projectile motion 3 Moion wih consn ccelerion: Liner nd projecile moion cons, In he precedin Lecure we he considered moion wih consn ccelerion lon he is: Noe h,, cn be posiie nd neie h leds o rie of behiors. Clerl similr

More information

HOMEWORK 6 - INTEGRATION. READING: Read the following parts from the Calculus Biographies that I have given (online supplement of our textbook):

HOMEWORK 6 - INTEGRATION. READING: Read the following parts from the Calculus Biographies that I have given (online supplement of our textbook): MAT 3 CALCULUS I 5.. Dokuz Eylül Uiversiy Fculy of Sciece Deprme of Mhemics Isrucors: Egi Mermu d Cell Cem Srıoğlu HOMEWORK 6 - INTEGRATION web: hp://kisi.deu.edu.r/egi.mermu/ Tebook: Uiversiy Clculus,

More information

(b) 10 yr. (b) 13 m. 1.6 m s, m s m s (c) 13.1 s. 32. (a) 20.0 s (b) No, the minimum distance to stop = 1.00 km. 1.

(b) 10 yr. (b) 13 m. 1.6 m s, m s m s (c) 13.1 s. 32. (a) 20.0 s (b) No, the minimum distance to stop = 1.00 km. 1. Answers o Een Numbered Problems Chper. () 7 m s, 6 m s (b) 8 5 yr 4.. m ih 6. () 5. m s (b).5 m s (c).5 m s (d) 3.33 m s (e) 8. ().3 min (b) 64 mi..3 h. ().3 s (b) 3 m 4..8 mi wes of he flgpole 6. (b)

More information

An object moving with speed v around a point at distance r, has an angular velocity. m/s m

An object moving with speed v around a point at distance r, has an angular velocity. m/s m Roion The mosphere roes wih he erh n moions wihin he mosphere clerly follow cure phs (cyclones, nicyclones, hurricnes, ornoes ec.) We nee o epress roion quniiely. For soli objec or ny mss h oes no isor

More information

Version 001 test-1 swinney (57010) 1. is constant at m/s.

Version 001 test-1 swinney (57010) 1. is constant at m/s. Version 001 es-1 swinne (57010) 1 This prin-ou should hve 20 quesions. Muliple-choice quesions m coninue on he nex column or pge find ll choices before nswering. CubeUniVec1x76 001 10.0 poins Acubeis1.4fee

More information

LEADER & ACHIEVER COURSE PHASE : MLA,MLB,MLC, MLD, MLE,MLF, MLG, MLH, MLI, MLJ, MAZA,MAZB & MAZC TARGET : PRE-MEDICAL 2016

LEADER & ACHIEVER COURSE PHASE : MLA,MLB,MLC, MLD, MLE,MLF, MLG, MLH, MLI, MLJ, MAZA,MAZB & MAZC TARGET : PRE-MEDICAL 2016 CSSRM CNTCT PRGRMME (cdeic Sessio : 05-06) EDER & CIEVER CURSE PSE : M,M,MC, MD, ME,MF, MG, M, MI, MJ, MZ,MZ & MZC Tes Type : MJR TRGET : PRE-MEDIC 06 Tes Per : IPMT TEST DTE : 07-04 - 06 TEST SYUS : SYUS

More information

Chapter 5: The pn Junction

Chapter 5: The pn Junction Cher 5: The ucio Noequilibrium ecess crriers i semicoducors Crrier geerio d recombiio Mhemicl lysis of ecess crriers Ambiolr rsor The jucio Bsic srucure of he jucio Zero lied bis Reverse lied bis No-uiformly

More information

Problems and Solutions for Section 3.2 (3.15 through 3.25)

Problems and Solutions for Section 3.2 (3.15 through 3.25) 3-7 Problems ad Soluios for Secio 3 35 hrough 35 35 Calculae he respose of a overdamped sigle-degree-of-freedom sysem o a arbirary o-periodic exciaio Soluio: From Equaio 3: x = # F! h "! d! For a overdamped

More information

Free Flapping Vibration of Rotating Inclined Euler Beams

Free Flapping Vibration of Rotating Inclined Euler Beams World cdemy of Sciece, Egieerig d Techology 56 009 Free Flppig Vibrio of Roig Iclied Euler Bems Chih-ig Hug, We-Yi i, d Kuo-Mo Hsio bsrc mehod bsed o he power series soluio is proposed o solve he url frequecy

More information

PHYSICS 1210 Exam 1 University of Wyoming 14 February points

PHYSICS 1210 Exam 1 University of Wyoming 14 February points PHYSICS 1210 Em 1 Uniersiy of Wyoming 14 Februry 2013 150 poins This es is open-noe nd closed-book. Clculors re permied bu compuers re no. No collborion, consulion, or communicion wih oher people (oher

More information

COLLABORATED AND CONSTRAINED NEURAL-EKF ALGORITHM FOR THE VESSEL TRAFFIC MONITORING AND INFORMATION SYSTEM

COLLABORATED AND CONSTRAINED NEURAL-EKF ALGORITHM FOR THE VESSEL TRAFFIC MONITORING AND INFORMATION SYSTEM Proceedigs o he 3 h Ieriol Coerece o Oce, Oshore d Arcic Egieerig OMAE11 Jue 19-4, 11, Roerdm, he Neherlds OMAE11-548 COLLABORAED AND CONSRAINED NEURAL-EKF ALGORIHM FOR HE VESSEL RAFFIC MONIORING AND INFORMAION

More information

Section 8. Paraxial Raytracing

Section 8. Paraxial Raytracing Secio 8 Paraxial aracig 8- OPTI-5 Opical Desig ad Isrmeaio I oprigh 7 Joh E. Greiveamp YNU arace efracio (or reflecio) occrs a a ierface bewee wo opical spaces. The rasfer disace ' allows he ra heigh '

More information

Average & instantaneous velocity and acceleration Motion with constant acceleration

Average & instantaneous velocity and acceleration Motion with constant acceleration Physics 7: Lecure Reminders Discussion nd Lb secions sr meeing ne week Fill ou Pink dd/drop form if you need o swich o differen secion h is FULL. Do i TODAY. Homework Ch. : 5, 7,, 3,, nd 6 Ch.: 6,, 3 Submission

More information

1. Solve by the method of undetermined coefficients and by the method of variation of parameters. (4)

1. Solve by the method of undetermined coefficients and by the method of variation of parameters. (4) 7 Differeial equaios Review Solve by he mehod of udeermied coefficies ad by he mehod of variaio of parameers (4) y y = si Soluio; we firs solve he homogeeous equaio (4) y y = 4 The correspodig characerisic

More information

t s (half of the total time in the air) d?

t s (half of the total time in the air) d? .. In Cl or Homework Eercie. An Olmpic long jumper i cpble of jumping 8.0 m. Auming hi horizonl peed i 9.0 m/ he lee he ground, how long w he in he ir nd how high did he go? horizonl? 8.0m 9.0 m / 8.0

More information

MTH 146 Class 11 Notes

MTH 146 Class 11 Notes 8.- Are of Surfce of Revoluion MTH 6 Clss Noes Suppose we wish o revolve curve C round n is nd find he surfce re of he resuling solid. Suppose f( ) is nonnegive funcion wih coninuous firs derivive on he

More information

6.003: Signals and Systems Lecture 20 April 22, 2010

6.003: Signals and Systems Lecture 20 April 22, 2010 6.003: Sigals ad Sysems Lecure 0 April, 00 6.003: Sigals ad Sysems Relaios amog Fourier Represeaios Mid-erm Examiaio #3 Wedesday, April 8, 7:30-9:30pm. No reciaios o he day of he exam. Coverage: Lecures

More information

Electromechanical System Dynamics, energy Conversion, and Electromechanical Analogies. Modeling of Dynamic Systems

Electromechanical System Dynamics, energy Conversion, and Electromechanical Analogies. Modeling of Dynamic Systems Elecroecicl Syse Dyics, eergy Coersio, d Elecroecicl Alogies Modelig of Dyic Syses Modelig of dyic syses y e doe i seerl wys: Use e sdrd equio of oio Newo s Lw for ecicl syses Use circuis eores O s lw

More information

Motion. Part 2: Constant Acceleration. Acceleration. October Lab Physics. Ms. Levine 1. Acceleration. Acceleration. Units for Acceleration.

Motion. Part 2: Constant Acceleration. Acceleration. October Lab Physics. Ms. Levine 1. Acceleration. Acceleration. Units for Acceleration. Moion Accelerion Pr : Consn Accelerion Accelerion Accelerion Accelerion is he re of chnge of velociy. = v - vo = Δv Δ ccelerion = = v - vo chnge of velociy elpsed ime Accelerion is vecor, lhough in one-dimensionl

More information

Review for the Midterm Exam.

Review for the Midterm Exam. Review for he iderm Exm Rememer! Gross re e re Vriles suh s,, /, p / p, r, d R re gross res 2 You should kow he disiio ewee he fesile se d he udge se, d kow how o derive hem The Fesile Se Wihou goverme

More information

Administrivia. Administrivia. Visual motion. CMPSCI 370: Intro. to Computer Vision. Optical flow

Administrivia. Administrivia. Visual motion. CMPSCI 370: Intro. to Computer Vision. Optical flow Admiisriia Fial eam: Thrsda, Ma 5, -3pm, Hasbrock 3 Reiew sessio poll Thrsda, April 8, 4-5pm, Locaio: TDB Tesda, Ma 3, 4-5pm, Locaio: TDB CMPSC 370: ro. o Comper Visio Reiew oes are posed o Moodle Opical

More information

Velocity is a relative quantity

Velocity is a relative quantity Veloci is a relaie quani Disenangling Coordinaes PHY2053, Fall 2013, Lecure 6 Newon s Laws 2 PHY2053, Fall 2013, Lecure 6 Newon s Laws 3 R. Field 9/6/2012 Uniersi of Florida PHY 2053 Page 8 Reference Frames

More information

Calculus BC 2015 Scoring Guidelines

Calculus BC 2015 Scoring Guidelines AP Calculus BC 5 Scorig Guidelies 5 The College Board. College Board, Advaced Placeme Program, AP, AP Ceral, ad he acor logo are regisered rademarks of he College Board. AP Ceral is he official olie home

More information

Reinforcement Learning

Reinforcement Learning Reiforceme Corol lerig Corol polices h choose opiml cios Q lerig Covergece Chper 13 Reiforceme 1 Corol Cosider lerig o choose cios, e.g., Robo lerig o dock o bery chrger o choose cios o opimize fcory oupu

More information

2 f(x) dx = 1, 0. 2f(x 1) dx d) 1 4t t6 t. t 2 dt i)

2 f(x) dx = 1, 0. 2f(x 1) dx d) 1 4t t6 t. t 2 dt i) Mah PracTes Be sure o review Lab (ad all labs) There are los of good quesios o i a) Sae he Mea Value Theorem ad draw a graph ha illusraes b) Name a impora heorem where he Mea Value Theorem was used i he

More information

Chapter 6 - Work and Energy

Chapter 6 - Work and Energy Caper 6 - Work ad Eergy Rosedo Pysics 1-B Eploraory Aciviy Usig your book or e iere aswer e ollowig quesios: How is work doe? Deie work, joule, eergy, poeial ad kieic eergy. How does e work doe o a objec

More information

The solution is often represented as a vector: 2xI + 4X2 + 2X3 + 4X4 + 2X5 = 4 2xI + 4X2 + 3X3 + 3X4 + 3X5 = 4. 3xI + 6X2 + 6X3 + 3X4 + 6X5 = 6.

The solution is often represented as a vector: 2xI + 4X2 + 2X3 + 4X4 + 2X5 = 4 2xI + 4X2 + 3X3 + 3X4 + 3X5 = 4. 3xI + 6X2 + 6X3 + 3X4 + 6X5 = 6. [~ o o :- o o ill] i 1. Mrices, Vecors, nd Guss-Jordn Eliminion 1 x y = = - z= The soluion is ofen represened s vecor: n his exmple, he process of eliminion works very smoohly. We cn elimine ll enries

More information

ENGR 1990 Engineering Mathematics The Integral of a Function as a Function

ENGR 1990 Engineering Mathematics The Integral of a Function as a Function ENGR 1990 Engineering Mhemics The Inegrl of Funcion s Funcion Previously, we lerned how o esime he inegrl of funcion f( ) over some inervl y dding he res of finie se of rpezoids h represen he re under

More information

Chapter 3 Kinematics in Two Dimensions

Chapter 3 Kinematics in Two Dimensions Chaper 3 KINEMATICS IN TWO DIMENSIONS PREVIEW Two-dimensional moion includes objecs which are moing in wo direcions a he same ime, such as a projecile, which has boh horizonal and erical moion. These wo

More information

Vibration damping of the cantilever beam with the use of the parametric excitation

Vibration damping of the cantilever beam with the use of the parametric excitation The s Ieraioal Cogress o Soud ad Vibraio 3-7 Jul, 4, Beijig/Chia Vibraio dampig of he cailever beam wih he use of he parameric exciaio Jiří TŮMA, Pavel ŠURÁNE, Miroslav MAHDA VSB Techical Uiversi of Osrava

More information

Kinematics in two dimensions

Kinematics in two dimensions Lecure 5 Phsics I 9.18.13 Kinemaics in wo dimensions Course websie: hp://facul.uml.edu/andri_danlo/teaching/phsicsi Lecure Capure: hp://echo36.uml.edu/danlo13/phsics1fall.hml 95.141, Fall 13, Lecure 5

More information

A Kalman filtering simulation

A Kalman filtering simulation A Klmn filering simulion The performnce of Klmn filering hs been esed on he bsis of wo differen dynmicl models, ssuming eiher moion wih consn elociy or wih consn ccelerion. The former is epeced o beer

More information

Review Equations. Announcements 9/8/09. Table Tennis

Review Equations. Announcements 9/8/09. Table Tennis Announcemens 9/8/09 1. Course homepage ia: phsics.bu.edu Class web pages Phsics 105 (Colon J). (Class-wide email sen) Iclicker problem from las ime scores didn ge recorded. Clicker quizzes from lecures

More information

Horizontal product differentiation: Consumers have different preferences along one dimension of a good.

Horizontal product differentiation: Consumers have different preferences along one dimension of a good. Produc Differeiio Firms see o e uique log some dimesio h is vlued y cosumers. If he firm/roduc is uique i some resec, he firm c commd rice greer h cos. Horizol roduc differeiio: Cosumers hve differe refereces

More information

Ideal Amplifier/Attenuator. Memoryless. where k is some real constant. Integrator. System with memory

Ideal Amplifier/Attenuator. Memoryless. where k is some real constant. Integrator. System with memory Liear Time-Ivaria Sysems (LTI Sysems) Oulie Basic Sysem Properies Memoryless ad sysems wih memory (saic or dyamic) Causal ad o-causal sysems (Causaliy) Liear ad o-liear sysems (Lieariy) Sable ad o-sable

More information

Solutions to selected problems from the midterm exam Math 222 Winter 2015

Solutions to selected problems from the midterm exam Math 222 Winter 2015 Soluios o seleced problems from he miderm eam Mah Wier 5. Derive he Maclauri series for he followig fucios. (cf. Pracice Problem 4 log( + (a L( d. Soluio: We have he Maclauri series log( + + 3 3 4 4 +...,

More information

KINEMATICS OF RIGID BODIES RELATIVE VELOCITY RELATIVE ACCELERATION PROBLEMS

KINEMATICS OF RIGID BODIES RELATIVE VELOCITY RELATIVE ACCELERATION PROBLEMS KINEMTICS OF RIGID ODIES RELTIVE VELOCITY RELTIVE CCELERTION PROLEMS 1. The crculr dsk rolls o he lef whou slppg. If.7 m s deerme he eloc d ccelero of he ceer O of he dsk. (516) .7 m s O? O? . The ed rollers

More information

The ray paths and travel times for multiple layers can be computed using ray-tracing, as demonstrated in Lab 3.

The ray paths and travel times for multiple layers can be computed using ray-tracing, as demonstrated in Lab 3. C. Trael me cures for mulple reflecors The ray pahs ad rael mes for mulple layers ca be compued usg ray-racg, as demosraed Lab. MATLAB scrp reflec_layers_.m performs smple ray racg. (m) ref(ms) ref(ms)

More information

Suggested Solution for Pure Mathematics 2011 By Y.K. Ng (last update: 8/4/2011) Paper I. (b) (c)

Suggested Solution for Pure Mathematics 2011 By Y.K. Ng (last update: 8/4/2011) Paper I. (b) (c) per I. Le α 7 d β 7. The α d β re he roos o he equio, such h α α, β β, --- α β d αβ. For, α β For, α β α β αβ 66 The seme is rue or,. ssume Cosider, α β d α β y deiiio α α α α β or some posiive ieer.

More information

Introduction to LoggerPro

Introduction to LoggerPro Inroducion o LoggerPro Sr/Sop collecion Define zero Se d collecion prmeers Auoscle D Browser Open file Sensor seup window To sr d collecion, click he green Collec buon on he ool br. There is dely of second

More information

Physics Worksheet Lesson 4: Linear Motion Section: Name:

Physics Worksheet Lesson 4: Linear Motion Section: Name: Physics Workshee Lesson 4: Liner Moion Secion: Nme: 1. Relie Moion:. All moion is. b. is n rbirry coorine sysem wih reference o which he posiion or moion of somehing is escribe or physicl lws re formule.

More information

LOCUS 1. Definite Integration CONCEPT NOTES. 01. Basic Properties. 02. More Properties. 03. Integration as Limit of a Sum

LOCUS 1. Definite Integration CONCEPT NOTES. 01. Basic Properties. 02. More Properties. 03. Integration as Limit of a Sum LOCUS Defiie egrio CONCEPT NOTES. Bsic Properies. More Properies. egrio s Limi of Sum LOCUS Defiie egrio As eplied i he chper iled egrio Bsics, he fudmel heorem of clculus ells us h o evlue he re uder

More information

Main Ideas in Class Today

Main Ideas in Class Today Main Ideas in Class Toda Inroducion o Falling Appl Consan a Equaions Graphing Free Fall Sole Free Fall Problems Pracice:.45,.47,.53,.59,.61,.63,.69, Muliple Choice.1 Freel Falling Objecs Refers o objecs

More information

Science Advertisement Intergovernmental Panel on Climate Change: The Physical Science Basis 2/3/2007 Physics 253

Science Advertisement Intergovernmental Panel on Climate Change: The Physical Science Basis   2/3/2007 Physics 253 Science Adeisemen Inegoenmenl Pnel on Clime Chnge: The Phsicl Science Bsis hp://www.ipcc.ch/spmfeb7.pdf /3/7 Phsics 53 hp://www.fonews.com/pojecs/pdf/spmfeb7.pdf /3/7 Phsics 53 3 Sus: Uni, Chpe 3 Vecos

More information

Decompression diagram sampler_src (source files and makefiles) bin (binary files) --- sh (sample shells) --- input (sample input files)

Decompression diagram sampler_src (source files and makefiles) bin (binary files) --- sh (sample shells) --- input (sample input files) . Iroduco Probblsc oe-moh forecs gudce s mde b 50 esemble members mproved b Model Oupu scs (MO). scl equo s mde b usg hdcs d d observo d. We selec some prmeers for modfg forecs o use mulple regresso formul.

More information

KINEMATICS OF RIGID BODIES RELATIVE VELOCITY RELATIVE ACCELERATION PROBLEMS

KINEMATICS OF RIGID BODIES RELATIVE VELOCITY RELATIVE ACCELERATION PROBLEMS KINEMTICS F RIGID DIES RELTIVE VELCITY RELTIVE CCELERTIN PRLEMS 1. The crculr dsk rolls o he lef whou slppg. If.7 m s deerme he eloc d ccelero of he ceer of he dsk. (516) .7 m s?? . The eloc of roller

More information

Time Dependent Queuing

Time Dependent Queuing Time Depede Queuig Mark S. Daski Deparme of IE/MS, Norhweser Uiversiy Evaso, IL 628 Sprig, 26 Oulie Will look a M/M/s sysem Numerically iegraio of Chapma- Kolmogorov equaios Iroducio o Time Depede Queue

More information

Supplement: Gauss-Jordan Reduction

Supplement: Gauss-Jordan Reduction Suppleme: Guss-Jord Reducio. Coefficie mri d ugmeed mri: The coefficie mri derived from sysem of lier equios m m m m is m m m A O d he ugmeed mri derived from he ove sysem of lier equios is [ ] m m m m

More information

ONE RANDOM VARIABLE F ( ) [ ] x P X x x x 3

ONE RANDOM VARIABLE F ( ) [ ] x P X x x x 3 The Cumulive Disribuio Fucio (cd) ONE RANDOM VARIABLE cd is deied s he probbiliy o he eve { x}: F ( ) [ ] x P x x - Applies o discree s well s coiuous RV. Exmple: hree osses o coi x 8 3 x 8 8 F 3 3 7 x

More information

INVESTMENT PROJECT EFFICIENCY EVALUATION

INVESTMENT PROJECT EFFICIENCY EVALUATION 368 Miljeko Crjac Domiika Crjac INVESTMENT PROJECT EFFICIENCY EVALUATION Miljeko Crjac Professor Faculy of Ecoomics Drsc Domiika Crjac Faculy of Elecrical Egieerig Osijek Summary Fiacial efficiecy of ivesme

More information

The sphere of radius a has the geographical form. r (,)=(acoscos,acossin,asin) T =(p(u)cos v, p(u)sin v,q(u) ) T.

The sphere of radius a has the geographical form. r (,)=(acoscos,acossin,asin) T =(p(u)cos v, p(u)sin v,q(u) ) T. Che 5. Dieeil Geome o Sces 5. Sce i meic om I 3D sce c be eeseed b. Elici om z =. Imlici om z = 3. Veco om = o moe geel =z deedig o wo mees. Emle. he shee o dis hs he geoghicl om =coscoscossisi Emle. he

More information

An Efficient Method to Reduce the Numerical Dispersion in the HIE-FDTD Scheme

An Efficient Method to Reduce the Numerical Dispersion in the HIE-FDTD Scheme Wireless Egieerig ad Techolog, 0,, 30-36 doi:0.436/we.0.005 Published Olie Jauar 0 (hp://www.scirp.org/joural/we) A Efficie Mehod o Reduce he umerical Dispersio i he IE- Scheme Jua Che, Aue Zhag School

More information

Pre-Calculus - Chapter 3 Sections Notes

Pre-Calculus - Chapter 3 Sections Notes Pre-Clculus - Chpter 3 Sectios 3.1-3.4- Notes Properties o Epoets (Review) 1. ( )( ) = + 2. ( ) =, (c) = 3. 0 = 1 4. - = 1/( ) 5. 6. c Epoetil Fuctios (Sectio 3.1) Deiitio o Epoetil Fuctios The uctio deied

More information

Big O Notation for Time Complexity of Algorithms

Big O Notation for Time Complexity of Algorithms BRONX COMMUNITY COLLEGE of he Ciy Uiversiy of New York DEPARTMENT OF MATHEMATICS AND COMPUTER SCIENCE CSI 33 Secio E01 Hadou 1 Fall 2014 Sepember 3, 2014 Big O Noaio for Time Complexiy of Algorihms Time

More information

Chapters 2 Kinematics. Position, Distance, Displacement

Chapters 2 Kinematics. Position, Distance, Displacement Chapers Knemacs Poson, Dsance, Dsplacemen Mechancs: Knemacs and Dynamcs. Knemacs deals wh moon, bu s no concerned wh he cause o moon. Dynamcs deals wh he relaonshp beween orce and moon. The word dsplacemen

More information

s in boxe wers ans Put

s in boxe wers ans Put Pu answers in boxes Main Ideas in Class Toda Inroducion o Falling Appl Old Equaions Graphing Free Fall Sole Free Fall Problems Pracice:.45,.47,.53,.59,.61,.63,.69, Muliple Choice.1 Freel Falling Objecs

More information

4-6 ROTATIONAL MOTION

4-6 ROTATIONAL MOTION Chpter 4 Motions in Spce 51 Reinforce the ide tht net force is needed for orbitl motion Content We discuss the trnsition from projectile motion to orbitl motion when bll is thrown horizontlly with eer

More information

Class 36. Thin-film interference. Thin Film Interference. Thin Film Interference. Thin-film interference

Class 36. Thin-film interference. Thin Film Interference. Thin Film Interference. Thin-film interference Thi Film Ierferece Thi- ierferece Ierferece ewee ligh waves is he reaso ha hi s, such as soap ules, show colorful paers. Phoo credi: Mila Zikova, via Wikipedia Thi- ierferece This is kow as hi- ierferece

More information

Section 8 Convolution and Deconvolution

Section 8 Convolution and Deconvolution APPLICATIONS IN SIGNAL PROCESSING Secio 8 Covoluio ad Decovoluio This docume illusraes several echiques for carryig ou covoluio ad decovoluio i Mahcad. There are several operaors available for hese fucios:

More information

Integration and Differentiation

Integration and Differentiation ome Clculus bckgroud ou should be fmilir wih, or review, for Mh 404 I will be, for he mos pr, ssumed ou hve our figerips he bsics of (mulivrible) fucios, clculus, d elemer differeil equios If here hs bee

More information

4.8 Improper Integrals

4.8 Improper Integrals 4.8 Improper Inegrls Well you ve mde i hrough ll he inegrion echniques. Congrs! Unforunely for us, we sill need o cover one more inegrl. They re clled Improper Inegrls. A his poin, we ve only del wih inegrls

More information

SECTION B Circular Motion

SECTION B Circular Motion SECTION B Circulr Motion 1. When person stnds on rotting merry-go-round, the frictionl force exerted on the person by the merry-go-round is (A) greter in mgnitude thn the frictionl force exerted on the

More information

Linear System Theory

Linear System Theory Naioal Tsig Hua Uiversiy Dearme of Power Mechaical Egieerig Mid-Term Eamiaio 3 November 11.5 Hours Liear Sysem Theory (Secio B o Secio E) [11PME 51] This aer coais eigh quesios You may aswer he quesios

More information

PI3B V, 16-Bit to 32-Bit FET Mux/DeMux NanoSwitch. Features. Description. Pin Configuration. Block Diagram.

PI3B V, 16-Bit to 32-Bit FET Mux/DeMux NanoSwitch. Features. Description. Pin Configuration. Block Diagram. 33V, 6-Bi o 32-Bi FET Mux/DeMux NaoSwich Feaures -ohm Swich Coecio Bewee Two Pors Near-Zero Propagaio Delay Fas Swichig Speed: 4s (max) Ulra -Low Quiesce Power (02mA yp) Ideal for oebook applicaios Idusrial

More information

General Relativity Fall 2018 Midterm exam, 11/13/2018

General Relativity Fall 2018 Midterm exam, 11/13/2018 Geerl Reliviy Fll 2018 Miderm exm 11/13/2018 NAME seful formuls d coss Chr el symbols µ 1 2 g @ µg + @ g µ @ g µ 1 A few coss i cgs u G 667 10 8 cm 3 g 1 s 2 c 300 10 10 cm s 1 M Su 199 10 33 g R Su 696

More information

Physics 201, Lecture 5

Physics 201, Lecture 5 Phsics 1 Lecue 5 Tod s Topics n Moion in D (Chp 4.1-4.3): n D Kinemicl Quniies (sec. 4.1) n D Kinemics wih Consn Acceleion (sec. 4.) n D Pojecile (Sec 4.3) n Epeced fom Peiew: n Displcemen eloci cceleion

More information

Experiment 6: Fourier Series

Experiment 6: Fourier Series Fourier Series Experime 6: Fourier Series Theory A Fourier series is ifiie sum of hrmoic fucios (sies d cosies) wih every erm i he series hvig frequecy which is iegrl muliple of some pricipl frequecy d

More information

22.615, MHD Theory of Fusion Systems Prof. Freidberg Lecture 10: The High Beta Tokamak Con d and the High Flux Conserving Tokamak.

22.615, MHD Theory of Fusion Systems Prof. Freidberg Lecture 10: The High Beta Tokamak Con d and the High Flux Conserving Tokamak. .615, MHD Theory of Fusion Sysems Prof. Freidberg Lecure 1: The High Be Tokmk Con d nd he High Flux Conserving Tokmk Proeries of he High Tokmk 1. Evlue he MHD sfey fcor: ψ B * ( ) 1 3 ρ 1+ ν ρ ρ cosθ *

More information

Existence Of Solutions For Nonlinear Fractional Differential Equation With Integral Boundary Conditions

Existence Of Solutions For Nonlinear Fractional Differential Equation With Integral Boundary Conditions Reserch Ivey: Ieriol Jourl Of Egieerig Ad Sciece Vol., Issue (April 3), Pp 8- Iss(e): 78-47, Iss(p):39-6483, Www.Reserchivey.Com Exisece Of Soluios For Nolier Frciol Differeil Equio Wih Iegrl Boudry Codiios,

More information

DIFFERENCE EQUATIONS

DIFFERENCE EQUATIONS DIFFERECE EQUATIOS Lier Cos-Coeffiie Differee Eqios Differee Eqios I disree-ime ssems, esseil feres of ip d op sigls pper ol speifi iss of ime, d he m o e defied ewee disree ime seps or he m e os. These

More information

Optical flow. Visual motion. Motion and perceptual organization. Motion and perceptual organization. Subhransu Maji. CMPSCI 670: Computer Vision

Optical flow. Visual motion. Motion and perceptual organization. Motion and perceptual organization. Subhransu Maji. CMPSCI 670: Computer Vision Visal moio Opical flow Sbhras Maji CMPSC 670: Comper Visio Ocober 0, 06 Ma slides adaped from S. Seiz, R. Szeliski, M. Pollefes CMPSC 670 Moio ad percepal orgaizaio Moio ad percepal orgaizaio Someimes,

More information

Let s express the absorption of radiation by dipoles as a dipole correlation function.

Let s express the absorption of radiation by dipoles as a dipole correlation function. MIT Deparme of Chemisry 5.74, Sprig 004: Iroducory Quaum Mechaics II Isrucor: Prof. Adrei Tokmakoff p. 81 Time-Correlaio Fucio Descripio of Absorpio Lieshape Le s express he absorpio of radiaio by dipoles

More information

Kinematics of Wheeled Robots

Kinematics of Wheeled Robots 1 Kinemaics of Wheeled Robos hps://www.ouube.com/wach?=gis41ujlbu 2 Wheeled Mobile Robos robo can hae one or more wheels ha can proide seering direcional conrol power eer a force agains he ground an ideal

More information

Simulation of Rapid Transfer Alignment Considering Body Flexure and Data Delay on Dynamic Base *

Simulation of Rapid Transfer Alignment Considering Body Flexure and Data Delay on Dynamic Base * Jourl of Aerouic Arouic d Aviio Serie A Vol.43 No.4 pp.261-268 (2011) 261 Simulio of Rpid Trfer Aligme Coiderig Body Flexure d D Dely o Dymic Be * Feg Qi ** Xigqu Zh d Yhu Zhg School of Aerouic d Arouic

More information

6.003: Signals and Systems

6.003: Signals and Systems 6.003: Sigals ad Sysems Lecure 8 March 2, 2010 6.003: Sigals ad Sysems Mid-erm Examiaio #1 Tomorrow, Wedesday, March 3, 7:30-9:30pm. No reciaios omorrow. Coverage: Represeaios of CT ad DT Sysems Lecures

More information

Two Dimensional Dynamics

Two Dimensional Dynamics Physics 11: Lecure 6 Two Dimensional Dynamics Today s lecure will coer Chaper 4 Exam I Physics 11: Lecure 6, Pg 1 Brie Reiew Thus Far Newon s Laws o moion: SF=ma Kinemaics: x = x + + ½ a Dynamics Today

More information

Union-Find Partition Structures Goodrich, Tamassia Union-Find 1

Union-Find Partition Structures Goodrich, Tamassia Union-Find 1 Uio-Fid Pariio Srucures 004 Goodrich, Tamassia Uio-Fid Pariios wih Uio-Fid Operaios makesex: Creae a sileo se coaii he eleme x ad reur he posiio sori x i his se uioa,b : Reur he se A U B, desroyi he old

More information

and v y . The changes occur, respectively, because of the acceleration components a x and a y

and v y . The changes occur, respectively, because of the acceleration components a x and a y Week 3 Reciaion: Chaper3 : Problems: 1, 16, 9, 37, 41, 71. 1. A spacecraf is raveling wih a veloci of v0 = 5480 m/s along he + direcion. Two engines are urned on for a ime of 84 s. One engine gives he

More information

PI3B

PI3B 234789023478902347890223478902347890234789022347890234789023478902234789023478902347890223478902 Feaures Near-Zero propagaio delay -ohm swiches coec ipus o oupus Fas Swichig Speed - 4s max Permis Ho Iserio

More information

2/5/2012 9:01 AM. Chapter 11. Kinematics of Particles. Dr. Mohammad Abuhaiba, P.E.

2/5/2012 9:01 AM. Chapter 11. Kinematics of Particles. Dr. Mohammad Abuhaiba, P.E. /5/1 9:1 AM Chper 11 Kinemic of Pricle 1 /5/1 9:1 AM Inroducion Mechnic Mechnic i Th cience which decribe nd predic he condiion of re or moion of bodie under he cion of force I i diided ino hree pr 1.

More information

Kinematics in two Dimensions

Kinematics in two Dimensions Lecure 5 Chaper 4 Phsics I Kinemaics in wo Dimensions Course websie: hp://facul.uml.edu/andri_danlo/teachin/phsicsi PHYS.141 Lecure 5 Danlo Deparmen of Phsics and Applied Phsics Toda we are oin o discuss:

More information

CHAPTER 2 KINEMATICS IN ONE DIMENSION ANSWERS TO FOCUS ON CONCEPTS QUESTIONS

CHAPTER 2 KINEMATICS IN ONE DIMENSION ANSWERS TO FOCUS ON CONCEPTS QUESTIONS Physics h Ediion Cunell Johnson Young Sdler Soluions Mnul Soluions Mnul, Answer keys, Insrucor's Resource Mnul for ll chpers re included. Compleed downlod links: hps://esbnkre.com/downlod/physics-h-ediion-soluions-mnulcunell-johnson-young-sdler/

More information

Two Dimensional Dynamics

Two Dimensional Dynamics Physics 11: Lecure 6 Two Dimensional Dynamics Today s lecure will coer Chaper 4 Saring Wed Sep 15, W-F oice hours will be in 3 Loomis. Exam I M oice hours will coninue in 36 Loomis Physics 11: Lecure 6,

More information

Integration of the equation of motion with respect to time rather than displacement leads to the equations of impulse and momentum.

Integration of the equation of motion with respect to time rather than displacement leads to the equations of impulse and momentum. Inegraion of he equaion of moion wih respec o ime raher han displacemen leads o he equaions of impulse and momenum. These equaions greal faciliae he soluion of man problems in which he applied forces ac

More information