Chapter 4 2D and 3D Motion

Save this PDF as:
 WORD  PNG  TXT  JPG

Size: px
Start display at page:

Download "Chapter 4 2D and 3D Motion"

Transcription

1 Chpe 4 D nd 3D Moon I. Defnon II. Poecle oon III. Unfo ccul oon IV. Non-unfo ccul oon V. Rele oon

2 Poon eco: eend fo he on of coodne e o he pcle. 4. k z 4. k z z I. Defnon Aee eloc: 4.3 k z Dplceen eco: epeen pcle poon chne dun cen e nel.

3 Innneou eloc: d zk d d d d d dz d k 4.4 -The decon of he nnneou eloc of pcle lw nen o he pcle ph he pcle poon Aee cceleon: 4.5 Innneou cceleon: z k d d d d d d d d z k 4.6

4 II. Poecle oon Moon of pcle lunched wh nl eloc, nd fee fll cceleon. The hozonl nd ecl oon e ndependen fo ech ohe. - Hozonl oon: = = = conn co 4.7 Rne R: hozonl dnce eled b poecle befoe eunn o lunch heh. - Vecl oon: = - = conn n 4.8 n 4.9 n 4.

5 - Teco: poecle ph. 4. co n co co n co Hozonl ne: R = - ; - =. 4. n co n co n co co n n co co R R R R R R R Mu fo lunch nle of 45º Oell upon: he houh whch he poecle oe h no effec on oon fcon neleced.

6 : A hd ben whe o how o f be, 7 fee dn. H be hown peed 85 h. If he how he bll hozonll 3 f boe he ound, how f fo f be wll h he ound? b Fo he e nl heh, wh upwd nle u he hd ben how he bll f he f ben o cch 3 f boe he ound? c Wh wll be he e of flh n h ce? h=3f B3 B B =38.7 h h foo 3 fee.9 h=3f Hozonl oeen Vecl oeen fo B B3 θ B The bll wll h ound.3 fo B 4.9 n co 38co n n co 38co n n 4.9

7 N7: In Glleo Two New Scence, he uho e h fo eleon nle of poecon whch eceed o fll ho of 45º b equl oun, he ne e equl Poe h een. θ=45º =R=R? n b n cob co n b n b n cob co n b R R' n 9 R R' n n co co9 h Rne : R n d 45 n9 45 n9 n n 9 co co9 n co co

8 III. Unfo ccul oon Moon ound ccle conn peed T n co n n n co n co co n p p p p du lon deced d d d d d d - Peod of eoluon: - Acceleon: cenpel -Veloc: nen o ccle n he decon of oon. Mnude of eloc nd cceleon conn. Decon e connuoul.

9 54. A c de e-o-ound whle unn wh unfo ccul oon. A e =, he c eloc : = 3+4, eued on n hozonl coodne e. A e =5 eloc : = Wh e he nude of he c cenpel cceleon nd b he c ee cceleon dun he e nel -? In 3 he eloc eeed he c eche he oppoe de of he ccle T c

10 IV. Non-Unfo ccul oon - A pcle oe wh n peed n ccul ph. - The cceleon h wo coponen: - Rdl =- c =- - Tnenl = dd - cue he chne n he peed of he pcle. d d - In unfo ccul oon, = conn = =

11 V. Rele oon Pcle eloc depend on efeence fe PA PB BA 4.5 D Fe oe conn eloc d d d d PA PB BA PA PB d d 4.6 Obee on dffeen fe of efeence eue he e cceleon fo on pcle f he ele eloc conn.

12 .5 flh flh lunch lnd flh b lunch lnd el, 75. A led oe n he nee decon peed whlebllofcehofoheledwheloc = + ele o he led. When he bll lnd, hozonl dplceen b ele o he ound fo lunch poon o lndn poon eued. The fue e b funcon of. Aue lnd ppoel lunch heh. Wh e he lue of nd b? The bll dplceen b ele o he led cn lo be eued. Aue h he led eloc no chned when he bll ho. Wh b when c 5 nd d 5? Lunch eloc ele o ound Dplceen ele o ound b flh flh.5 b b = + b b flh Dplceen ele o he led Rele o he led, he dplceen doe no depend on he led peed Anwe c= Anwe d flh b 4 4

13 A do whe o co e o pon decl oppoe hown. I cn w n ll we nd he e flown. A wh nle wh epec o he lne onn he n nd fnhn pon hould wn? fnh f θ f n co n 3 n co f co f f 3

14 A pcle oe wh conn peed ound he ccle below. When pon A coodne e =, =3 nd eloc 5. Wh e eloc nd cceleon pon B? Epe ou nwe n e of un eco. B B 5 B B A 8.3 A 5

15 . A hn lde 7.5 boe ound leel wh eloc of 8 n nle of 3º below he hozonl nd conn cceleon of, up. Aue = he nn u decbed nd we n equon fo he eleon of he hn lde funcon of, wh = ound leel. b Ue he equon o deene he lue of when =. c Epln wh hee e wo oluon o p B. Whch one epeen he e ke he hn lde o ech ound leel? d how f doe he hn lde el hozonll dun he nel beween = nd he e eche he ound? Fo he e nl poon nd eloc, wh conn cceleon wll cue he hn lde o ech ound leel wh zeo eloc? Epe ou nwe n e of un eco , 3 h=7.5 3º = 8 8co 3 o 8n If he ound w no old, he lde would woop down, pn houh he ufce, hen bck up n, wh he wo e of pn ben =3, =5. d Vecl oeen : f f f Hozonl oeen :

16 4. A bll o be ho fo leel ound wh cen peed. The fue below how he ne R wll he eu he lunch nle θ whch cn be lunched. The choce of θ deene he flh e; le epeen he u flh e. Wh he le peed he bll wll he dun flh f θ choen uch h he flh e.5? R flh.5 n 4.9 n n n n.5 n.5 3 θ The lowe peed occu he op of he eco hlf of ol e of flh, when he eloc h pl n -coponen. n hlf eco co3 fo. 5 Gph R 4 fo 45 R n n 4 n co

Physics 110 Spring 2006 Rotational Dynamics Their Solutions

Physics 110 Spring 2006 Rotational Dynamics Their Solutions Phyc 0 Spng 006 Roonl Dync The Soluon. An objec o e nd oe couneclockwe wh conn ngul cceleon nd eche n ngul peed o / n. Wh he ngul cceleon o he wheel? Wh he ngle (n n hough whch he objec oe n h e? α α θ

More information

Vector Algebra. Lecture programme. Engineering Maths 1.2

Vector Algebra. Lecture programme. Engineering Maths 1.2 Leue pogmme Engneeng Mh. Veo lge Conen of leue. Genel noduon. Sl nd veo. Cen omponen. Deon one. Geome epeenon. Modulu of veo. Un veo. Pllel veo.. ddon of veo: pllelogm ule; ngle lw; polgon lw; veo lw fo

More information

B y R us se ll E ri c Wr ig ht, DV M. M as te r of S ci en ce I n V et er in ar y Me di ca l Sc ie nc es. A pp ro ve d:

B y R us se ll E ri c Wr ig ht, DV M. M as te r of S ci en ce I n V et er in ar y Me di ca l Sc ie nc es. A pp ro ve d: E ff ec ts o f El ec tr ic al ly -S ti mu la te d Si lv er -C oa te d Im pl an ts a nd B ac te ri al C on ta mi na ti on i n a Ca ni ne R ad iu s Fr ac tu re G ap M od el B y R us se ll E ri c Wr ig ht,

More information

AP Physics Gravity and Circular Motion

AP Physics Gravity and Circular Motion AP Phyic Gity nd icul Motion Newton theoy i ey iple. Gity i foce of ttction between ny two object tht he. Two object itting on dektop ttct ech othe with foce tht we cll gity. They don t go flying togethe

More information

Chapter 10. Rotational Kinematics

Chapter 10. Rotational Kinematics Chape 10. Roaonal Knemacs Up o now we hae only consdeed ponpacles.e. we hae no consdeed he shape o sze only he mass Also we hae only consdeed he moon o pon-pacles sagh-lne ee-all pojecle moon. Bu eal objecs

More information

Kinematics Review Checklist

Kinematics Review Checklist Kinemics Reiew Checklis Vecors n Sclrs 1.1.0 Gie exmples of ecors n sclrs; n recognize he ifference beween hem. Wh wo prs oes ecor he? Which of hese prs comprises sclr? Which of he following re ecors?

More information

Homework 3. problems: 4.5, 4.31, 4.49, 4.67

Homework 3. problems: 4.5, 4.31, 4.49, 4.67 Hoewok 3 poble: 4.5, 4.3, 4.49, 4.67 Poble 4.5 The veco poiion of a paicle vaie in ie accoding o he expeion ( 3. ˆi 6. ˆj ). (a) Find expeion fo he velociy and acceleaion a funcion of ie. (b) Deeine he

More information

Physics 110 Spring 2006 Forces in 1- and 2-Dimensions Their Solutions

Physics 110 Spring 2006 Forces in 1- and 2-Dimensions Their Solutions Phic 110 Spring 006 orce in 1- nd -Dienion heir Solution 1. wo orce 1 nd ct on 5kg. I the gnitude o 1 nd re 0 nd 15 repectivel wht re the ccelertion o ech o the e elow?.. 0; ( 0 ) + ( 15 ) 1 5kg 15 @ θ

More information

A ball rolls up and down an incline A ball tossed up which comes down along the same path

A ball rolls up and down an incline A ball tossed up which comes down along the same path Lecure 4 Moion nd Kinemics Reiew Turning Poins Inerpreing Moion Grphs Ls ime we lef off lking bou ccelerion nd urning poins. Recll ccelerion is wh chnges n iniil elociy o finl elociy. A chnge in elociy

More information

Mr. Kepple. Motion at Constant Acceleration 1D Kinematics HW#5. Name: Date: Period: (b) Distance traveled. (a) Acceleration.

Mr. Kepple. Motion at Constant Acceleration 1D Kinematics HW#5. Name: Date: Period: (b) Distance traveled. (a) Acceleration. Moion Consn Accelerion 1D Kinemics HW#5 Mr. Kepple Nme: De: Period: 1. A cr cceleres from 1 m/s o 1 m/s in 6.0 s. () Wh ws is ccelerion? (b) How fr did i rel in his ime? Assume consn ccelerion. () Accelerion

More information

PHYSICS 161 EXAM III: Thursday December 04, 2003 11:00 a.m.

PHYSICS 161 EXAM III: Thursday December 04, 2003 11:00 a.m. PHYS 6: Eam III Fall 003 PHYSICS 6 EXAM III: Thusda Decembe 04, 003 :00 a.m. Po. N. S. Chan. Please pn ou name and ene ou sea numbe o den ou and ou eamnaon. Suden s Pned Name: Recaon Secon Numbe: Sea Numbe:.

More information

E M C P e r f o r m a n c e R e q u i r e m e n t s C o m p o n e n t s

E M C P e r f o r m a n c e R e q u i r e m e n t s C o m p o n e n t s D a i m l e r C h r y s l e r D C -1 0 6 1 4 J o i n t E n g i n e e r i n g S t a n d a r d D a t e P u b l i s h e d : 2 0 0 5-03 C h r y s l e r C a t e g o r y : L -2 T ot a l N o. of Pa g e s ( I

More information

M I L I TARY SPEC I F I CAT I ON A I RPLANE STRENGTH ANO R I G I D I TY OATA AND REPORTS

M I L I TARY SPEC I F I CAT I ON A I RPLANE STRENGTH ANO R I G I D I TY OATA AND REPORTS mm L - A - 88688 ( AS ) ANENOMENT 24 MAY 99 M L TARY SPEC F CAT ON A RPLANE STRENGTH ANO R G D TY OATA AND REPORTS Th s amendmen t f o r ms a pa r t o f M L - A - 8868, da t ed 20 Ma y 987, and s app r

More information

Campus Sustainability Assessment and Related Literature

Campus Sustainability Assessment and Related Literature Campus Sustainability Assessment and Related Literature An Annotated Bibliography and Resource Guide Andrew Nixon February 2002 Campus Sustainability Assessment Review Project Telephone: (616) 387-5626

More information

1.- L a m e j o r o p c ió n e s c l o na r e l d i s co ( s e e x p li c a r á d es p u é s ).

1.- L a m e j o r o p c ió n e s c l o na r e l d i s co ( s e e x p li c a r á d es p u é s ). PROCEDIMIENTO DE RECUPERACION Y COPIAS DE SEGURIDAD DEL CORTAFUEGOS LINUX P ar a p od e r re c u p e ra r nu e s t r o c o rt a f u e go s an t e un d es a s t r e ( r ot u r a d e l di s c o o d e l a

More information

Payor Sheet for Medicare Part D/ PDP and MA-PD

Payor Sheet for Medicare Part D/ PDP and MA-PD Payor Specification Sheet for MEDICARE PART D/PDP AND MA-PD PRIME THERAPEUTICS LLC CLIENTS JANUARY 1, 2006 (Page 1 of 8) BIN: PCN: See BINs on page 2 (in bold red type) See PCNs on page 2 (in bold red

More information

Answer, Key Homework 4 David McIntyre Mar 25,

Answer, Key Homework 4 David McIntyre Mar 25, Answer, Key Homework 4 Dvid McIntyre 45123 Mr 25, 2004 1 his print-out should hve 18 questions. Multiple-choice questions my continue on the next column or pe find ll choices before mkin your selection.

More information

University Physics AI No. 1 Rectilinear Motion

University Physics AI No. 1 Rectilinear Motion Uniesity Physics AI No. Rectiline Motion Clss Numbe Nme I.Choose the Coect Answe. An object is moing long the is with position s function of time gien by (. Point O is t. The object is efinitely moing

More information

AP QUIZ #2 GRAPHING MOTION 1) POSITION TIME GRAPHS DISPLACEMENT Each graph below shows the position of an object as a function of time.

AP QUIZ #2 GRAPHING MOTION 1) POSITION TIME GRAPHS DISPLACEMENT Each graph below shows the position of an object as a function of time. AP QUIZ # GRAPHING MOTION ) POSITION TIME GRAPHS DISPLAEMENT Ech grph below shows the position of n object s function of time. A, B,, D, Rnk these grphs on the gretest mgnitude displcement during the time

More information

Practice Writing the Letter A

Practice Writing the Letter A Aa Practice Writing the Letter A A a A a Write a in the blank to finish each word. c t re h d Write A in the blank to finish each word. nn US ndy Bb Practice Writing the Letter B B b B l P b Write b in

More information

ú Ó Á É é ú ú É ú Á Á ú É É É ú É Ó É ó É Á ú ú ó Á Á ú Ó ú Ó ú É Á ú Á ú ó ú Á ú Á É Á Á Ó É Á ú ú é ú ú ú ú Á ú ó ú Ó Á Á Á Á ú ú ú é É ó é ó ú ú ú É é ú ú ú óú ú ú Ó Á ú ö é É ú ú ú úé ú ú É É Á É

More information

Applications of the Laplace Transform

Applications of the Laplace Transform EE 4G Noe: hper 6 nrucor: heung Applcon of he plce Trnform Applcon n rcu Anly. evew of eve Nework Elemen Superpoon Pge 6 PDF reed wh dekpdf PDF Wrer Trl :: hp://www.docudek.com EE 4G Noe: hper 6 nrucor:

More information

Java Community Process Executive Committee Meeting

Java Community Process Executive Committee Meeting Jv Cun P Exuv C Mng Supplnl S 15 Ob 4 Db 2009 Ppd f 8 Db 2009 b Hh VnCu 2C 0 u n Updd JSR JSR 332: JSR Rvw El Cln API f Jv ME * Cld 30 Nvb JSR 326: El Df Rvw P M JVM Dgn API Cld 28 Nvb JSR 299: Ppd Fnl

More information

C o a t i a n P u b l i c D e b tm a n a g e m e n t a n d C h a l l e n g e s o f M a k e t D e v e l o p m e n t Z a g e bo 8 t h A p i l 2 0 1 1 h t t pdd w w wp i j fp h D p u b l i c2 d e b td S t

More information

Answer, Key Homework 6 David McIntyre 45123 Mar 25, 2004 1

Answer, Key Homework 6 David McIntyre 45123 Mar 25, 2004 1 Answe, Key Homewok 6 vid McInye 4513 M 5, 004 1 This pin-ou should hve 0 quesions. Muliple-choice quesions my coninue on he nex column o pge find ll choices befoe mking you selecion. The due ime is Cenl

More information

Generalized Difference Sequence Space On Seminormed Space By Orlicz Function

Generalized Difference Sequence Space On Seminormed Space By Orlicz Function Ieaoa Joa of Scece ad Eee Reeach IJSER Vo Ie Decembe -4 5687 568X Geeazed Dffeece Seece Sace O Semomed Sace B Ocz Fco A.Sahaaa Aa ofeo G Ie of TechooCombaoeIda. Abac I h aewe defe he eece ace o emomed

More information

Orbits and Kepler s Laws

Orbits and Kepler s Laws Obits nd Keple s Lws This web pge intoduces some of the bsic ides of obitl dynmics. It stts by descibing the bsic foce due to gvity, then consides the ntue nd shpe of obits. The next section consides how

More information

Dispersion Relation and Wave Loads on a Vertical Cylinder in Water due to First Order Diffraction

Dispersion Relation and Wave Loads on a Vertical Cylinder in Water due to First Order Diffraction Dspeson Relon nd Wve Lods on Vecl Clnde n We due o s Ode Dffcon Dbu B Absc Hee we consde e fs ode wve dffcon b clndcl sucue. Te clndcl sucue s ccul vecl sufce pecn n we of fne dep. s we se e bound vlue

More information

T e s t e xp re s s i o n B o d y o f i f E xi t F i g u re 1 - F l o w c h art o f th e i f s tate m M u l ti S tate m s i n th e i f B o d y : L ik

T e s t e xp re s s i o n B o d y o f i f E xi t F i g u re 1 - F l o w c h art o f th e i f s tate m M u l ti S tate m s i n th e i f B o d y : L ik MQL4 COURSE By Coders guru w w w. f orex -t sd. c om -6- Loops & Decisions Part 2 ---------------------------- We l c o m e t o t h e s ix t h l e s s o n in m y c o u r s e a b o u t M Q L 4. I h o pe

More information

for SAB Chorus, Oboe & Piano Music by David L. Brunner -» T L m \ =L=L r\ r ftf M ff' ^ ' 1 * / s * irf r / mp -a ^ J ^ J p^- I will a- rise

for SAB Chorus, Oboe & Piano Music by David L. Brunner -» T L m \ =L=L r\ r ftf M ff' ^ ' 1 * / s * irf r / mp -a ^ J ^ J p^- I will a- rise Text by Wlla Butle Yeat Cooned o t 25th nveay by the Captal Dtct Youth Choale, Dane Wane, Founde Decto THE LKE ISLE OF INNISFREE o SB Chou, Oboe & Pano Muc by Davd L. Bunne Oboe Sopano lto Modeate = 96

More information

Lesson 6.1 Exercises, pages

Lesson 6.1 Exercises, pages Lesson 6. Eercises, pages 7 80 A. Use technolog to determine the value of each trigonometric ratio to the nearest thousandth. a) sin b) cos ( 6 ) c) cot 7 d) csc 8 0.89 0. tan 7 sin 8 0..0. Sketch each

More information

Lesson 8.1 Areas of Rectangles and Parallelograms

Lesson 8.1 Areas of Rectangles and Parallelograms Leon 8.1 e of Rectngle nd Pllelogm 1. Find the e of the hded egion.. Find the e of the hded egion. 17 cm 9 cm 5 cm 8 cm 1.5 cm 13 cm cm cm 3. Rectngle D h e 684 m nd width 44 m. Find it length. 4. Find.

More information

Circle Geometry (Part 3)

Circle Geometry (Part 3) Eam aer 3 ircle Geomery (ar 3) emen andard:.4.(c) yclic uadrilaeral La week we covered u otheorem 3, he idea of a convere and we alied our heory o ome roblem called IE. Okay, o now ono he ne chunk of heory

More information

Lesson 8.1 Areas of Rectangles and Parallelograms

Lesson 8.1 Areas of Rectangles and Parallelograms Leon 8.1 Ae of Rectngle nd Pllelogm In Eecie 1 4, find the e of the hded egion. 1.. 1 1 cm 3. 17 cm 4. 9 cm 5 cm 1.5 cm cm 5. Rectngle ABCD h e 684 m nd width 44 m. Find it length. 6. Dw pllelogm with

More information

Phys222 W12 Quiz 2: Chapters 23, 24. Name: = 80 nc, and q = 30 nc in the figure, what is the magnitude of the total electric force on q?

Phys222 W12 Quiz 2: Chapters 23, 24. Name: = 80 nc, and q = 30 nc in the figure, what is the magnitude of the total electric force on q? Nme: 1. A pricle (m = 5 g, = 5. µc) is relesed from res when i is 5 cm from second pricle (Q = µc). Deermine he mgniude of he iniil ccelerion of he 5-g pricle.. 54 m/s b. 9 m/s c. 7 m/s d. 65 m/s e. 36

More information

APPLYING LINGUISTIC PROMETHEE METHOD IN INVESTMENT PORTFOLIO DECISION-MAKING

APPLYING LINGUISTIC PROMETHEE METHOD IN INVESTMENT PORTFOLIO DECISION-MAKING Inenaonal Jounal of Eleconc Bune Managemen, Vol. 9, No., pp. 39-48 (0 39 PPLYING LINGUISTI PROMETHEE METHOD IN INVESTMENT PORTFOLIO DEISION-MKING hen-tung hen *, We-Zhan Hung and Hu-Lng heng 3 Depamen

More information

ASTR 170! 2010 S1 " Daniel Zucker! E7A 317 Mathematics as a tool for understanding physics

ASTR 170! 2010 S1  Daniel Zucker! E7A 317 Mathematics as a tool for understanding physics A New Scientific Er Grity nd Tides ASTR 170! 2010 S1 " Dniel Zucker! E7A 317 Mthemtics s tool for understnding physics zucker@science.mq.edu.u! 1 2 Velocity nd Accelertion Isc Newton (1643-1727)! Building

More information

v T R x m Version PREVIEW Practice 7 carroll (11108) 1

v T R x m Version PREVIEW Practice 7 carroll (11108) 1 Version PEVIEW Prctice 7 crroll (08) his print-out should he 5 questions. Multiple-choice questions y continue on the next colun or pge find ll choices before nswering. Atwood Mchine 05 00 0.0 points A

More information

Worked Examples. v max =?

Worked Examples. v max =? Exaple iction + Unifo Cicula Motion Cicula Hill A ca i diing oe a ei-cicula hill of adiu. What i the fatet the ca can die oe the top of the hill without it tie lifting off of the gound? ax? (1) Copehend

More information

Overview of Spellings on www.spellzoo.co.uk

Overview of Spellings on www.spellzoo.co.uk Overview of Spellings on www.spellzoo.co.uk Year 1 Set 1: CVC words Set 2: CVC and CCVC words Set 3: CVC, CCVC and CCVCC words Set 4: Words containing 'ch', 'sh', 'th' and 'wh' Set 5: Words ending in 'll',

More information

Version 001 Summer Review #03 tubman (IBII20142015) 1

Version 001 Summer Review #03 tubman (IBII20142015) 1 Version 001 Summer Reiew #03 tubmn (IBII20142015) 1 This print-out should he 35 questions. Multiple-choice questions my continue on the next column or pge find ll choices before nswering. Concept 20 P03

More information

Web Ul Design. Drupal Customization of Community Portal. Neurovation Creativity Tool ... ... ... _...,

Web Ul Design. Drupal Customization of Community Portal. Neurovation Creativity Tool ... ... ... _..., F uj nqu U D gn Po o o&s dwo O w o h o ow ng o omd 805 3G Au Pfi n g 28 www j nqu fl u D opm n W bd gn V u on mob W bu D gn n o m ong ph KnowCon n A nap h un pp om pp now on n n d3 87 86987 1? m =8 n uppo

More information

English Made Easy: Foundation Book 2 Notes for parents

English Made Easy: Foundation Book 2 Notes for parents nh M y: Fnn 2 pn h b n hp y ch p h cnn h n b nn. h chn, n n ncn c n h p h b nc y ch cy h n h p; n nc n h hp n pnn ; n y nn h pn c nn n h w h w p. h c w nc y ch h cy h n n n nn n. h cn p h b n hp y ch p

More information

Homework Solutions Unit 4: Chapter 22 CMPSC 465

Homework Solutions Unit 4: Chapter 22 CMPSC 465 Homeok Solution Unit : Chapte CMPSC 65 Diclaime: Thi i a daft of olution that ha been pepaed b the TA and the intucto make no guaantee that olution peented hee contain the leel of detail that ould be expected

More information

Exam FM/2 Interest Theory Formulas

Exam FM/2 Interest Theory Formulas Exm FM/ Iere Theory Formul by (/roprcy Th collboro of formul for he ere heory eco of he SO Exm FM / S Exm. Th uy hee free o-copyrghe ocume for ue g Exm FM/. The uhor of h uy hee ug ome oo h uque o h o

More information

Positive Integral Operators With Analytic Kernels

Positive Integral Operators With Analytic Kernels Çnky Ünverte Fen-Edeyt Fkülte, Journl of Art nd Scence Sy : 6 / Arl k 006 Potve ntegrl Opertor Wth Anlytc Kernel Cn Murt D KMEN Atrct n th pper we contruct exmple of potve defnte ntegrl kernel whch re

More information

In Going to my Naked Bed

In Going to my Naked Bed n Gg k B P Richrd Edwrds < n q n q < 5 g k sid sid mr g g k sid sid mr p i sw n t, pr < < d, k, prce, ful,, d, k, prce, ful,, n kg < k qh d, k, prce, ful,, s r lrd st k d, k, prce, qh ful,, s r wh g lrd

More information

stichting mathematisch centrum

stichting mathematisch centrum A stichting mathematisch centrum AFDELING INFORMATICA IV 2/73 FEBRUARY L,G.L,Tho MEERTENS and J X V A N VLiE T REPAIRING THE PARENTHESIS SKELETON 15F ALGOL 6 8 PROGRAMS A 2e boerhaavestraat 49 amsterdam

More information

finish line dr 1 L 1 v b v r finish line.

finish line dr 1 L 1 v b v r finish line. Answer, Key { Homewor { Rubn H Landau 1 Ths prn-ou should have 1 quesons. Chec ha s complee before leavng he prner. Also, mulple-choce quesons may connue on he nex column or page: nd all choces before

More information

Uniform Rectilinear Motion

Uniform Rectilinear Motion Engineeing Mechanics : Dynamics Unifom Rectilinea Motion Fo paticle in unifom ectilinea motion, the acceleation is zeo and the elocity is constant. d d t constant t t 11-1 Engineeing Mechanics : Dynamics

More information

Lines and Angles. 2. Straight line is a continuous set of points going on forever in both directions:

Lines and Angles. 2. Straight line is a continuous set of points going on forever in both directions: Lines nd Angles 1. Point shows position. A 2. Stright line is continuous set of points going on forever in oth directions: 3. Ry is line with one endpoint. The other goes on forever. G 4. Line segment

More information

Outline Presentation Why S c i r u s S c i r u s V a l u e C ha i n A d d e d v a l u e f o r E S a n d s c i e n t i f i c c o m m u n i t y

Outline Presentation Why S c i r u s S c i r u s V a l u e C ha i n A d d e d v a l u e f o r E S a n d s c i e n t i f i c c o m m u n i t y Searching the Scientific Web: s & T d s m m u Sciru he ad ed benefits fo r the cientific co nity Femke Markus S r. P ro d uc t Man ag er S c i rus 1 8 O c t o b er 2 0 0 2, C E R N, G en ev a Outline Presentation

More information

Bengali *P44319A0116* P44319A. Pearson Edexcel International GCSE. Wednesday 3 June 2015 Morning Time: 3 hours. Instructions. Information.

Bengali *P44319A0116* P44319A. Pearson Edexcel International GCSE. Wednesday 3 June 2015 Morning Time: 3 hours. Instructions. Information. Write your name here Surname Other names Pearson Edexcel International GCSE Bengali Centre Number Candidate Number Wednesday 3 June 2015 Morning Time: 3 hours You do not need any other materials. Paper

More information

B I N G O B I N G O. Hf Cd Na Nb Lr. I Fl Fr Mo Si. Ho Bi Ce Eu Ac. Md Co P Pa Tc. Uut Rh K N. Sb At Md H. Bh Cm H Bi Es. Mo Uus Lu P F.

B I N G O B I N G O. Hf Cd Na Nb Lr. I Fl Fr Mo Si. Ho Bi Ce Eu Ac. Md Co P Pa Tc. Uut Rh K N. Sb At Md H. Bh Cm H Bi Es. Mo Uus Lu P F. Hf Cd Na Nb Lr Ho Bi Ce u Ac I Fl Fr Mo i Md Co P Pa Tc Uut Rh K N Dy Cl N Am b At Md H Y Bh Cm H Bi s Mo Uus Lu P F Cu Ar Ag Mg K Thomas Jefferson National Accelerator Facility - Office of cience ducation

More information

Scope and Sequence - Synthetic Phonics Schedule

Scope and Sequence - Synthetic Phonics Schedule Correspondences () Kindy/Prep/Pre-Primary Kindy/Prep/Pre-Primary Term 1 Basic Code Power 1 Getting to Grips with Handwriting s m c t g p a o I, the, was, to, are, she Reading and beginning to spell Vocabulary

More information

Spline. Computer Graphics. B-splines. B-Splines (for basis splines) Generating a curve. Basis Functions. Lecture 14 Curves and Surfaces II

Spline. Computer Graphics. B-splines. B-Splines (for basis splines) Generating a curve. Basis Functions. Lecture 14 Curves and Surfaces II Lecure 4 Curves and Surfaces II Splne A long flexble srps of meal used by drafspersons o lay ou he surfaces of arplanes, cars and shps Ducks weghs aached o he splnes were used o pull he splne n dfferen

More information

Enterprise Data Center A c h itec tu re Consorzio Operativo Gruppo MPS Case S t u d y : P r o g et t o D i sast er R ec o v er y Milano, 7 Febbraio 2006 1 Il G r u p p o M P S L a B a n c a M o n t e d

More information

CROSS REFERENCE. Cross Reference Index 110-122. Cast ID Number 110-111 Connector ID Number 111 Engine ID Number 112-122. 2015 Ford Motor Company 109

CROSS REFERENCE. Cross Reference Index 110-122. Cast ID Number 110-111 Connector ID Number 111 Engine ID Number 112-122. 2015 Ford Motor Company 109 CROSS REFERENCE Cross Reference Index 110-122 Cast ID Number 110-111 Connector ID Number 111 112-122 2015 Ford Motor Company 109 CROSS REFERENCE Cast ID Number Cast ID Ford Service # MC Part # Part Type

More information

Hubs. Hubs. Agricultural Hubs:

Hubs. Hubs. Agricultural Hubs: Hubs Hubs Our hubs, spindles and wheels are produced under the same roof at our 100,000 sq. ft. plant and work seamlessly together. We manufacture a wide range of hubs our experienced group of engineers

More information

Homework 3 Solution Chapter 3.

Homework 3 Solution Chapter 3. Homework 3 Solution Chpter 3 2 Let Q e the group of rtionl numers under ddition nd let Q e the group of nonzero rtionl numers under multiplition In Q, list the elements in 1 2 In Q, list the elements in

More information

Generator stability analysis - Fractional tools application

Generator stability analysis - Fractional tools application Generor by ny - Frcon oo ppcon Auhor : Ocvn ENACHEANU Dephne RIU Nco RETIERE SDNE Grenobe -67 Oune. Eecrc nework cone. Frcon moeng o ynchronou mchne. Se pce repreenon n by conon o ynchronou mchne neger

More information

NAMA FILM Aleksinackih rudara 39A 11070 Beograd, Serbia Tel/Fax:+381 11 2 603 762 Mobile: +381 63 206440 princip@eunet.rs www.goranradovanovic.

NAMA FILM Aleksinackih rudara 39A 11070 Beograd, Serbia Tel/Fax:+381 11 2 603 762 Mobile: +381 63 206440 princip@eunet.rs www.goranradovanovic. SYNOPSIS T h e A m b u l a n c e i s a c o n t e m p o r a r y h i s t o r i c a l f i l m r e f l e c t i n g t h e d r a m a o f t h e p r o f o u n d s o c i a l c h a n g e s t h a t t h e S e r b

More information

With Rejoicing Hearts/ Con Amor Jovial. A Fm7 B sus 4 B Cm Cm7/B

With Rejoicing Hearts/ Con Amor Jovial. A Fm7 B sus 4 B Cm Cm7/B for uli With Rejoic Herts/ on mor ol dition # 10745-Z1 ime ortez Keyord ccompniment y effy Honoré INTRO With energy ( = c 88) Keyord * m7 B sus 4 B 7/B mj 9 /B SMPL B 7 *Without percussion, egin he 1995,

More information

Chapter 3 - Vectors. I. Definition. Arithmetic operations involving vectors. A) Addition and subtraction

Chapter 3 - Vectors. I. Definition. Arithmetic operations involving vectors. A) Addition and subtraction Chpter 3 - Vectors I. Defnton II. Arthmetc opertons nvolvng vectors A Aton n sutrcton - Grphcl metho - Anltcl metho Vector components B Multplcton Revew of ngle reference sstem 9º º

More information

B A S I C S C I E N C E S

B A S I C S C I E N C E S B A S I C S C I E N C E S 10 B A S I C S C I E N C E S F I R S T S E M E S T E R C O U R S E S : H U M A N S T R U C T U R E A N D F U N C T I O N [ H S F I ] M O L E C U L A R B A S I S O F M E D I C

More information

Jesus Performed Miracles

Jesus Performed Miracles F Jonl P Ju Pr Mircl ch f lo Al n fri r b f Li blo n of ick li on Po k r u yi li br o n o y o on y r v y o r b f ch rfriror n -ll cr r p r o y k li Tor n of o ll y r u o kn on r ch n L ch p Ju Hl Officil

More information

Put the human back in Human Resources.

Put the human back in Human Resources. Put the human back in Human Resources A Co m p l et e Hu m a n Ca p i t a l Ma n a g em en t So l u t i o n t h a t em p o w er s HR p r o f essi o n a l s t o m eet t h ei r co r p o r a t e o b j ect

More information

Math 1105: Calculus II (Math/Sci majors) MWF 11am / 12pm, Campion 235 Written homework 5

Math 1105: Calculus II (Math/Sci majors) MWF 11am / 12pm, Campion 235 Written homework 5 Mth 5: Clculus II Mth/Sci mjos) MWF m / pm, Cmpion 35 Witten homewok 5 6.6, p. 458 3,33), 6.7, p. 467 8,3), 6.875), 7.58,6,6), 7.44,48) Fo pctice not to tun in): 6.6, p. 458,8,,3,4), 6.7, p. 467 4,6,8),

More information

Chapter 3 - Vectors. Arithmetic operations involving vectors. A) Addition and subtraction. - Graphical method - Analytical method Vector components

Chapter 3 - Vectors. Arithmetic operations involving vectors. A) Addition and subtraction. - Graphical method - Analytical method Vector components Chpter 3 - Vectors I. Defnton II. Arthmetc opertons nvolvng vectors A) Addton nd sutrcton - Grphcl method - Anltcl method Vector components B) Multplcton Revew of ngle reference sstem 90º

More information

How is phonics taught in our school? Wednesday 23 rd September 2015

How is phonics taught in our school? Wednesday 23 rd September 2015 Phonics? How is phonics taught in our school? Wednesday 23 rd September 2015 What is phonics? What is phonics? Phonics is a way of teaching children to read quickly and skilfully. They are taught how to:

More information

1. Oblast rozvoj spolků a SU UK 1.1. Zvyšování kvalifikace Školení Zapojení do projektů Poradenství 1.2. Financování 1.2.1.

1. Oblast rozvoj spolků a SU UK 1.1. Zvyšování kvalifikace Školení Zapojení do projektů Poradenství 1.2. Financování 1.2.1. 1. O b l a s t r o z v o j s p o l k a S U U K 1. 1. Z v y š o v á n í k v a l i f i k a c e Š k o l e n í o S t u d e n t s k á u n i e U n i v e r z i t y K a r l o v y ( d á l e j e n S U U K ) z í

More information

! www.ukuleleorcstr.com Tse re T Ukulele Orcstr of ret Br s sets prticipti pieces ecember 2016 USA Sesl shows. Tse sets show mt of mic. Wn co lg ply wh Orcstr, might hve fun nd do m differently, different

More information

Sound Discovery Jaz Ampaw-Farr - Which Phonics 2013 2

Sound Discovery Jaz Ampaw-Farr - Which Phonics 2013 2 1 Sound Discovery 2 Learning to Read and Write Phoneme Awareness EAL ow ay s igh ea or Grapheme Knowledge Phonics Screening Check = 1 in 2 chance after 2 years. 3 Phonics Teaching Core Criteria n n n n

More information

YRRTC Business Plan

YRRTC Business Plan 2015 2025 YRRTC Business Plan 2015 annual update updated 2015 edocs #5677831 mission Our mission is to design and deliver an exceptional rapid transit system attracting, moving and connecting people to

More information

EASY RECEPTION TASKS FOR USE IN THE LITERACY HOUR. S t e p h e n s t e. Jigsaw names of self and friends.

EASY RECEPTION TASKS FOR USE IN THE LITERACY HOUR. S t e p h e n s t e. Jigsaw names of self and friends. EASY RECEPTION TASKS FOR USE IN THE LITERACY HOUR Own Nme Tk Mtching letter underneth nme crd. S t e p h e n t e B e n Mtching mgnetic letter under nme crd p t t h o n Jigw nme of elf nd friend. T r c

More information

Basically, logarithmic transformations ask, a number, to what power equals another number?

Basically, logarithmic transformations ask, a number, to what power equals another number? Wht i logrithm? To nwer thi, firt try to nwer the following: wht i x in thi eqution? 9 = 3 x wht i x in thi eqution? 8 = 2 x Biclly, logrithmic trnformtion k, number, to wht power equl nother number? In

More information

Hour Exam No.1. p 1 v. p = e 0 + v^b. Note that the probe is moving in the direction of the unit vector ^b so the velocity vector is just ~v = v^b and

Hour Exam No.1. p 1 v. p = e 0 + v^b. Note that the probe is moving in the direction of the unit vector ^b so the velocity vector is just ~v = v^b and Hou Exam No. Please attempt all of the following poblems befoe the due date. All poblems count the same even though some ae moe complex than othes. Assume that c units ae used thoughout. Poblem A photon

More information

Physics 110 Spring D Motion Problems and their Solutions

Physics 110 Spring D Motion Problems and their Solutions Phyc 1 Sprng 006 1-D Moton Proble and ther Soluton 1. Jule Verne n 1865 propoed endng people to the oon by rng a pace capule ro a 0- long cannon wth a nal elocty o.97 k/. What the acceleraton o th pace

More information

7' RICOCHET SHUFFLEBOARD TABLE

7' RICOCHET SHUFFLEBOARD TABLE 7' RICOCHET SHUFFLEBOARD TABLE ASSEM BLYL INSTRUCTIONS NG1201 THANK Y OU! Th a n k yo u f o r p u r ch a si n g t h i s p r o d u ct. We w o r k a r o u n d t h e cl o ck a n d a r o u n d t h e g l o

More information

South East of Process Main Building / 1F. North East of Process Main Building / 1F. At 14:05 April 16, 2011. Sample not collected

South East of Process Main Building / 1F. North East of Process Main Building / 1F. At 14:05 April 16, 2011. Sample not collected At 14:05 April 16, 2011 At 13:55 April 16, 2011 At 14:20 April 16, 2011 ND ND 3.6E-01 ND ND 3.6E-01 1.3E-01 9.1E-02 5.0E-01 ND 3.7E-02 4.5E-01 ND ND 2.2E-02 ND 3.3E-02 4.5E-01 At 11:37 April 17, 2011 At

More information

Solution to Problem Set 1

Solution to Problem Set 1 CSE 5: Introduction to the Theory o Computtion, Winter A. Hevi nd J. Mo Solution to Prolem Set Jnury, Solution to Prolem Set.4 ). L = {w w egin with nd end with }. q q q q, d). L = {w w h length t let

More information

Transformations. Computer Graphics. Types of Transformations. 2D Scaling from the origin. 2D Translations. 9/22/2011. Geometric Transformation

Transformations. Computer Graphics. Types of Transformations. 2D Scaling from the origin. 2D Translations. 9/22/2011. Geometric Transformation 9// anfomaion. Compue Gaphic Lecue anfomaion Wha i a anfomaion? Wha oe i o? anfom he cooinae / nomal veco of objec Wh ue hem? Moelling -Moving he objec o he eie locaion in he envionmen -Muliple inance

More information

Lecture 3 1/16. Torque on a Dipole. The magnitude of the torque: center of mass. Fsin F -Q. dipole moment. torque points into the page

Lecture 3 1/16. Torque on a Dipole. The magnitude of the torque: center of mass. Fsin F -Q. dipole moment. torque points into the page Lectue 3 /6 Toque on Dipole F F sin The mgnitude of the toque: Fsin d Fsin psin p ( d Fsin d qsin F - d F θ cente of mss dipole moment p q d toque points into the pge Lectue 3 /6 uiz uestion An electic

More information

C A R I N G / F A I R N E S S GRADE: KINDERGARTEN

C A R I N G / F A I R N E S S GRADE: KINDERGARTEN C A R I N G / F A I R N E S S GRADE: KINDERGARTEN Core Cu rri c u lu m : Su pp l em ents social stu d i e s Foc u s : In terpers onal skill s, ch a racter bu i l d i n g Overvi ew: E m p a t hy is the

More information

Key Stage 1 Phonics & Spelling. Programme (linked with Floppy s Phonics and New Curriculum) Year 1

Key Stage 1 Phonics & Spelling. Programme (linked with Floppy s Phonics and New Curriculum) Year 1 *See also specifications regarding phonics in reading in the new curriculum (word reading) Year 1 The sounds /f/, /l/, /s/, /z/, and /k/ spelt ff, ll, ss, zz and ck Phase 2 Revisit Stage 1+ Book 5 and

More information

CSE202 Greedy algorithms

CSE202 Greedy algorithms CSE0 Greedy algorihm . Shore Pah in a Graph hore pah from Princeon CS deparmen o Einein' houe . Shore Pah in a Graph hore pah from Princeon CS deparmen o Einein' houe Tree wih a mo edge G i a ree on n

More information

Chattanooga Choo Choo

Chattanooga Choo Choo 3 Ooe (Eng Horn) oon Alto Sax 1 Alto Sax 2 Tenor Sax 1 Tenor Sax 2 Baritone Sax Horn Horn 3 Trumet Trumet 3 Tromone Tromone 3 Tua q = 155 Sing & n n n m & Perc 1 Electric HarTACET Fe 1, 2011 q = 155 Sing

More information

Sounds. All words are made up of sounds. In English there are 44

Sounds. All words are made up of sounds. In English there are 44 Sounds All words are made up of sounds In English there are 44 How does it work? Children: Learn 44 sounds and matching letters/letter groups Learn to blend sounds to read words Read lots of specially

More information

COMPLETELY RANDOM DESIGN (CRD) -Design can be used when experimental units are essentially homogeneous.

COMPLETELY RANDOM DESIGN (CRD) -Design can be used when experimental units are essentially homogeneous. COMPLETEL RANDOM DESIGN CRD Descpon of he Desgn -Smples desgn o use. -Desgn can be used when expemenal uns ae essenally homogeneous. -Because of he homogeney equemen, may be dffcul o use hs desgn fo feld

More information

XII. By a fountaine where I lay, CANTUS.

XII. By a fountaine where I lay, CANTUS. 4 8 12 X. founte whe, CNTUS. d- 1. te whe 2. fire grce, Fire tht h nd might sh- clene lnds ll high oke dy glt hev'n- bl,, Ws de bles round- Cme Plid John Dowlnd s ll - te gr- nee, true loves be Hp-, heven-

More information

N V V L. R a L I. Transformer Equation Notes

N V V L. R a L I. Transformer Equation Notes Tnsfome Eqution otes This file conts moe etile eivtion of the tnsfome equtions thn the notes o the expeiment 3 wite-up. t will help you to unestn wht ssumptions wee neee while eivg the iel tnsfome equtions

More information

Copthill School. Information for Parents on Read Write Inc.

Copthill School. Information for Parents on Read Write Inc. Copthill School Information for Parents on Read Write Inc. What is the purpose of this handout? To inform parents of how reading is taught at Copthill To supply parents with clear information on the RWI

More information

BLADE 12th Generation. Rafał Olszewski. Łukasz Matras

BLADE 12th Generation. Rafał Olszewski. Łukasz Matras BLADE 12th Generation Rafał Olszewski Łukasz Matras Jugowice, 15-11-2012 Gl o b a l M a r k e t i n g Dell PowerEdge M-Series Blade Server Portfolio M-Series Blades couple powerful computing capabilities

More information

what is the probability that an item fails before a specified time?

what is the probability that an item fails before a specified time? 7 Relably There are varous ssues n relably We have already looked a deermnng he relably of a sysem f he relables of s componens are known Here we are neresed n he me ll falure of pars Informaon abou falure

More information

Steps in solving heredity problems:

Steps in solving heredity problems: Seps in solving herediy problems: Monohybrid crosses I. Boh prens re heerozygous The llele of brown eyes is inheried s n uosoml dominn llele. If boh prens re heerozygous, wh is he probbiliy h hey cn hve

More information

Online Department Stores. What are we searching for?

Online Department Stores. What are we searching for? Online Department Stores What are we searching for? 2 3 CONTENTS Table of contents 02 Table of contents 03 Search 06 Fashion vs. footwear 04 A few key pieces 08 About SimilarWeb Stepping up the Competition

More information

Interconnect Delay Models

Interconnect Delay Models Inerconnec elay Models Basc rcu Analyss echnques Ouu resonse For lnear crcus: N + F Basc waeforms Se nu Pulse nu Imulse Inu Newor srucures & sae Inu waeform & zero-saes Use smle nu waeforms o undersand

More information

Belgian Onion Soup 6.50 German Potato Pancakes Charcuterie Plate

Belgian Onion Soup 6.50 German Potato Pancakes Charcuterie Plate OUP & APPTIZR Okbf Pz u Of Th Day Wh Hu Ba 4.95 mk amn mu an a vgab am h h gman mua a an bgan nv 95 Bgan Onn u 6.50 Gman Pa Panak Chau Pa v wh u am 7.95 n f u ma an auag gman aam mk fam auag wfaan ham

More information

Construction. Entry 1 Reading. Module: Health and safety signs. Module Aims. Main aim We are learning what some health and safety signs mean.

Construction. Entry 1 Reading. Module: Health and safety signs. Module Aims. Main aim We are learning what some health and safety signs mean. Couco Ey 1 Rdg Modu: Hh d fy g Modu Am M m W g wh om hh d fy g m. Oh g m W g h mg of wod d ymbo o hh d fy g. Modu: Hh d fy g Am: W g wh om hh d fy g m. Th dff kd of fy g. Bu cc you wh you mu do. Thy cd

More information