(This lesson plan assumes the students are using an air-powered rocket as described in the Materials section.)

Save this PDF as:
 WORD  PNG  TXT  JPG

Size: px
Start display at page:

Download "(This lesson plan assumes the students are using an air-powered rocket as described in the Materials section.)"

Transcription

1 The Mah Projecs Journal Page 1 PROJECT MISSION o MArs inroducion Many sae mah sandards and mos curricula involving quadraic equaions require sudens o solve "falling objec" or "projecile" problems, which involve equaions dealing wih graviy. This lesson allows he sudens o experience he relevance of hese equaions by acually launching rockes and calculaing he maximum heigh of heir flighs. The lesson leads he sudens from he experienial o he absrac by using he daa and high ineres conex of he aciviy o analyze he criical componens of quadraic equaions. daa collecion and predicions (This lesson plan assumes he sudens are using an air-powered rocke as described in he Maerials secion.) Before aking he sudens o he launch sie, explain he logisics and safey procedures. Each group of four will have a "somper," "loader," "imer," and "recorder." The loader places he rocke on he launcher. Jus as a safey measure, he loader should never place his/her face over he launcher. The imer should sar he wach once hey see he somper jump on he launch pad, and should sop i once he rocke his he ground. This is done wice by each group and recorded on he suden handou. I is suggesed ha he eacher have wo Somp Rocke Launchers available, and have groups sanding in line for he wo launch saions. Once he sudens are back in class, hey are o 1) describe and skech he physical pah of he rocke, 2) skech he relaionship of he rocke's ime and heigh, which allows he eacher o discuss he difference beween hese wo parabolas, and finally 3) predic he maximum heigh of he rocke (by insinc, no calculaion, ye). Conceps Wriing, graphing and solving quadraic equaions; finding he verex and roos Time: 3 Hours Maerials Air Rockes, which can be made in he classroom and fueled by an air compressor, or can be purchased for approximaely $10 a mos oy sores. The oy versions involve jumping on an air bladder ha propels he rocke upward (Air Power Rockes by Valen Bros Game Co a Toys R US, or Somp Rockes by D&L) Preparaion This lesson is inended o be a summary lesson of quadraics. Sudens should already have a familiariy wih he algorihms involved in solving and graphing quadraics. The eacher will need o choose a venue for he launches. A large area such as he school's fooball field is suggesed. firs launch 4. The sudens should firs ponder he concree meanings of he verex, roos, and y-inercep. a) The ypical somp rocke is 1.5 fee long. Since he wach sops once he ip of he rocke his he ground, hen he iniial heigh is he heigh of he ip of he rocke a launch: 1.5 fee. b) The heigh a he end of he fligh is 0. c) The highes poin will be reached a approximaely half of he oal ime. This is only an esimae since he rocke does no sar a heigh zero. d) The sudens will know all variables excep he iniial velociy. SUBMITTED BY: Dr. Tom Benne, California Sae Universiy San Marcos; David Maoon, Poer Junior High; Ginny Jackson, Chaparral High School; Rober Fizparick & Chris Shore, Grea Oak High School MATH-123

2 The Mah Projecs Journal Page 2 PROJECT Mission o MArs (coninued) 5. By plugging in zero for h() and he recorded ime for, he sudens solve he only unknown variable, iniial velociy, and hen rewrie he equaion in sandard quadraic form. Once his is done, he sudens use he equaion o deermine a able of values and graph his equaion. They should be able o esimae maximum heigh from he graph. second launch This is an assessmen of he sudens' working knowledge of he aciviy. They are asked o use he second fligh ime o conduc all he same calculaions ha hey did wih he firs. This should be done as independenly as possible, wih minimal eacher assisance, in order o check for undersanding. rocke launch analysis Up o his poin he lesson has been focused on concree applicaions of quadraics. This nex and final phase focuses on he absrac meanings of he quadraics componens: verex, roos, y-inercep and soluions. The suden is asked o relae hese componens o he fligh of he rocke as well as he graph. These quesions are imporan for he sudens' concepual undersanding of parabolas and should be srongly emphasized by he eacher hrough class discussion. 7. By using he using he well-known formula x = -b/(2a), sudens can find he coordinaes of he verex, and compare i o heir predicions. 8. By seing he equaion equal o zero, he sudens ge wo values. One of which is he ime ha he rocke his he ground. Bu wha is his oher value, and why is i negaive? I is he oher ime when he rocke was a heigh zero or should we say, would have been a zero. I is negaive, because a ime zero, he rocke was already a a heigh of 1.5 fee. If we were o follow he graph back in ime (hus, he negaive roo), we see when he rocke would have hypoheically launched from heigh zero. 9. The y-inercep can be seen direcly in he equaion and should be 1.5 fee he iniial heigh of he rocke a ime zero. 10. The sudens evaluae for y given x = 2. Have sudens plo his poin. 11. The sudens se he equaion equal o 10 and solve. This gives conex o wha i means o solve for x given y. There are wo soluions because he rocke is en fee off he ground wice! Why is here only one soluion for #10? Have sudens plo boh soluions. 12. The sudens should ge an imaginary soluion. There are no real roos because he rocke really does no go ha high MATH-123

3 The Mah Projecs Journal Page 3 MISSION Have you ever launched a rocke or hrown a ball as hard as you can - sraigh up? Ever wonder how high i wen? Le's find ou! You are o launch a rocke and ime how long he rocke akes o reurn o earh. For he sake of he aciviy, you will need wo launches. Be sure ha you launch wice and record boh imes. Launch Time (seconds) o MArs Firs Trial Second Trial 1. Observe he behavior of he rocke as i is being launched and raveling hrough he air. Describe how he rocke ascends, urns and descends. Also, skech he pah of he rocke below. h 2. Skech wha you hink he graph of he heigh of he rocke (range) versus ime (domain) looks like. d h 3. How high do you hink your rocke wen?

4 The Mah Projecs Journal Page 4 Mission o MArs: Firs LAunch The formula for he rocke fligh is h() = v 0 - ½ g 2 + h 0, where... h() = heigh v 0 = iniial velociy = ime h 0 = iniial heigh g = he force of graviy (32 f/sec 2 ) 4. a) Wha is he heigh a he beginning of he fligh? b) Wha is he heigh a he end of he fligh? c) When will he highes poin of he fligh occur? d) There is a poin during he fligh when we know all he variables, excep one unknown? Wha is ha variable? 5. a) Use your fligh ime o calculae your iniial velociy, v 0. h() = v 0 - ½ g 2 + h 0 Disance (f) 200 b) For your rocke's fligh, wrie he equaion relaing ime o heigh. h() = c) Wha is he independen variable (domain)? Wha is he dependen variable (range)? d) Once you have calculaed your iniial velociy, complee he able of values for he equaion. Be sure o include he daa for your launch and land poins h() h() e) Graph hese ordered pairs. f) How high did your rocke fly? Time (sec)

5 The Mah Projecs Journal Page 5 Mission o MArs: SECOND LAunch 6. a) When will he highes poin of he fligh occur? b) Use your fligh ime o calculae your iniial velociy, v 0. h() = v 0 + h 0 c) For your rocke's fligh, wrie he equaion relaing ime o heigh. h() = d) Once you have calculaed your iniial velociy, make a able of values for he equaion. Choose your domain in erms of 0.5 seconds inervals. (i.e. = 0.5, 1.0, 1.5, 2.0, 2.5). Be sure o include he daa for your launch and land poins. Disance (f) h() h() e) Graph hese ordered pairs f) How high did your rocke fly? Time (sec)

6 The Mah Projecs Journal Page 6 Mission o MArs: rocket AnAlysis Given he equaion of your second rocke: h() = 7. a) Wha is he verex of his equaion? (, ) b) Wha do he coordinaes of his poin represen in regards o he fligh of he rocke? c) Where on he graph is his poin found? 8. a) Wha are he roos of he equaion? (, ) & (, ) b) Wha do he roos represen in regards o he fligh of he rocke? c) Why is one of he roos negaive? d) Where on he graph are hese poins found?

7 The Mah Projecs Journal Page 7 Mission o MArs: rocket AnAlysis (coninued) 9. a) Wha is he y-inercep of his equaion? (, ) b) Wha do he coordinaes of his poin represen in regards o he fligh of he rocke? c) Where on he graph is his poin found? 10. How high will he rocke be afer 2 seconds? f 11. a) When will he rocke be 10 fee off he ground? sec b) Why are here wo soluions? 12. a) When will he rocke be 500 fee off he ground? sec b) Why are here no real soluions?

Lab 3 Acceleration. What You Need To Know: Physics 211 Lab

Lab 3 Acceleration. What You Need To Know: Physics 211 Lab b Lab 3 Acceleraion Wha You Need To Know: The Physics In he previous lab you learned ha he velociy of an objec can be deermined by finding he slope of he objec s posiion vs. ime graph. x v ave. = v ave.

More information

The student will create simulations of vertical components of circular and harmonic motion on GX.

The student will create simulations of vertical components of circular and harmonic motion on GX. Learning Objecives Circular and Harmonic Moion (Verical Transformaions: Sine curve) Algebra ; Pre-Calculus Time required: 10 150 min. The sudens will apply combined verical ranslaions and dilaions in he

More information

P. Bruschi: Project guidelines PSM Project guidelines.

P. Bruschi: Project guidelines PSM Project guidelines. Projec guidelines. 1. Rules for he execuion of he projecs Projecs are opional. Their aim is o improve he sudens knowledge of he basic full-cusom design flow. The final score of he exam is no affeced by

More information

NCTM Content Standard/National Science Education Standard:

NCTM Content Standard/National Science Education Standard: Tile: Logarihms Brief Overview: In his Concep Developmen Uni, he concep of logarihms is discussed. The relaionship beween eponenial equaions and logarihmic equaions is eplored. The properies of logs are

More information

Notes on the Fourier Transform

Notes on the Fourier Transform Noes on he Fourier Transform The Fourier ransform is a mahemaical mehod for describing a coninuous funcion as a series of sine and cosine funcions. The Fourier Transform is produced by applying a series

More information

Grade 8 Math: Final Exam Review Unit 6: Linear Equations and Graphing

Grade 8 Math: Final Exam Review Unit 6: Linear Equations and Graphing Lesson 6.: Solving Equaions Using Models. Use a model o solve each equaion. Verif he soluion. a) 7 = 56 b) 45 = 9 c) = 4 d) 9 =. Use a model o solve each equaion. Verif he soluion. a) 5 + 4 = 44 b) 7 +

More information

Extra Practice 1. Name Date. Lesson 6.1: Solving Equations Using Models

Extra Practice 1. Name Date. Lesson 6.1: Solving Equations Using Models Maser 6.0 Era Pracice Lesson 6.: Solving Equaions Using Models. Use a model o solve each equaion. Verif he soluion. a) 7 = 56 b) 45 = 9 c) = 4 d) 9 =. Use a model o solve each equaion. Verif he soluion.

More information

4.5 Biasing in BJT Amplifier Circuits

4.5 Biasing in BJT Amplifier Circuits 4/5/011 secion 4_5 Biasing in MOS Amplifier Circuis 1/ 4.5 Biasing in BJT Amplifier Circuis eading Assignmen: 8086 Now le s examine how we C bias MOSFETs amplifiers! f we don bias properly, disorion can

More information

Mathematics Stage 5 PAS5.2.5 Graphs of physical phenomena. Distance/time graphs

Mathematics Stage 5 PAS5.2.5 Graphs of physical phenomena. Distance/time graphs Mahemaics Sage 5 PAS5.2.5 Graphs of physical phenomena Par 2 Disance/ime graphs Number: 43664 Tile: PAS5.2.5 Graphs of physical phenomena This publicaion is copyrigh New Souh Wales Deparmen of Eucaion

More information

Lines and Angles Notes Geometry Unit 3: Lesson 1. Parallel lines. Skew lines. Parallel planes. Transversal. Alternate Interior Angles t

Lines and Angles Notes Geometry Unit 3: Lesson 1. Parallel lines. Skew lines. Parallel planes. Transversal. Alternate Interior Angles t Lines and Angles Noes Geoery Uni 3: Lesson 1 Nae Parallel lines D C Skew lines A B Parallel planes E H F G Transversal Alernae Inerior Angles, 4 1 2 3 l Alernae Exerior Angles, 5 6 8 7 Corresponding Angles,,,

More information

Lecture #7: Discrete-time Signals and Sampling

Lecture #7: Discrete-time Signals and Sampling EEL335: Discree-Time Signals and Sysems Lecure #7: Discree-ime Signals and Sampling. Inroducion Lecure #7: Discree-ime Signals and Sampling Unlike coninuous-ime signals, discree-ime signals have defined

More information

Extra Practice 1. Name Date. Lesson 6.1: Solving Equations Using Models

Extra Practice 1. Name Date. Lesson 6.1: Solving Equations Using Models Name Dae Maser 6.0 Era Pracice Lesson 6.: Solving Equaions Using Models. Use a model o solve each equaion. Verif he soluion. a) 7 = 56 b) 45 = 9 c) = 4 d) 9 =. Use a model o solve each equaion. Verif he

More information

Memorandum on Impulse Winding Tester

Memorandum on Impulse Winding Tester Memorandum on Impulse Winding Teser. Esimaion of Inducance by Impulse Response When he volage response is observed afer connecing an elecric charge sored up in he capaciy C o he coil L (including he inside

More information

Negative frequency communication

Negative frequency communication Negaive frequency communicaion Fanping DU Email: dufanping@homail.com Qing Huo Liu arxiv:2.43v5 [cs.it] 26 Sep 2 Deparmen of Elecrical and Compuer Engineering Duke Universiy Email: Qing.Liu@duke.edu Absrac

More information

MEASUREMENTS OF VARYING VOLTAGES

MEASUREMENTS OF VARYING VOLTAGES MEASUREMENTS OF ARYING OLTAGES Measuremens of varying volages are commonly done wih an oscilloscope. The oscilloscope displays a plo (graph) of volage versus imes. This is done by deflecing a sream of

More information

16.5 ADDITIONAL EXAMPLES

16.5 ADDITIONAL EXAMPLES 16.5 ADDITIONAL EXAMPLES For reiew purposes, more examples of boh piecewise linear and incremenal analysis are gien in he following subsecions. No new maerial is presened, so readers who do no need addiional

More information

A-LEVEL Electronics. ELEC4 Programmable Control Systems Mark scheme June Version: 1.0 Final

A-LEVEL Electronics. ELEC4 Programmable Control Systems Mark scheme June Version: 1.0 Final A-LEVEL Elecronics ELEC4 Programmable Conrol Sysems scheme 243 June 26 Version:. Final schemes are prepared by he Lead Assessmen Wrier and considered, ogeher wih he relevan quesions, by a panel of subjec

More information

Signals and the frequency domain ENGR 40M lecture notes July 31, 2017 Chuan-Zheng Lee, Stanford University

Signals and the frequency domain ENGR 40M lecture notes July 31, 2017 Chuan-Zheng Lee, Stanford University Signals and he requency domain ENGR 40M lecure noes July 3, 07 Chuan-Zheng Lee, Sanord Universiy signal is a uncion, in he mahemaical sense, normally a uncion o ime. We oen reer o uncions as signals o

More information

Teacher Supplement to Operation Comics, Issue #5

Teacher Supplement to Operation Comics, Issue #5 eacher Supplemen o Operaion Comics, Issue #5 he purpose of his supplemen is o provide conen suppor for he mahemaics embedded ino he fifh issue of Operaion Comics, and o show how he mahemaics addresses

More information

The University of Melbourne Department of Mathematics and Statistics School Mathematics Competition, 2013 JUNIOR DIVISION Time allowed: Two hours

The University of Melbourne Department of Mathematics and Statistics School Mathematics Competition, 2013 JUNIOR DIVISION Time allowed: Two hours The Universiy of Melbourne Deparmen of Mahemaics and Saisics School Mahemaics Compeiion, 203 JUNIOR DIVISION Time allowed: Two hours These quesions are designed o es your abiliy o analyse a problem and

More information

ECE-517 Reinforcement Learning in Artificial Intelligence

ECE-517 Reinforcement Learning in Artificial Intelligence ECE-517 Reinforcemen Learning in Arificial Inelligence Lecure 11: Temporal Difference Learning (con.), Eligibiliy Traces Ocober 8, 2015 Dr. Iamar Arel College of Engineering Deparmen of Elecrical Engineering

More information

EE 40 Final Project Basic Circuit

EE 40 Final Project Basic Circuit EE 0 Spring 2006 Final Projec EE 0 Final Projec Basic Circui Par I: General insrucion 1. The final projec will coun 0% of he lab grading, since i s going o ake lab sessions. All oher individual labs will

More information

ECE3204 Microelectronics II Bitar / McNeill. ECE 3204 / Term D-2017 Problem Set 7

ECE3204 Microelectronics II Bitar / McNeill. ECE 3204 / Term D-2017 Problem Set 7 EE3204 Microelecronics II Biar / McNeill Due: Monday, May 1, 2017 EE 3204 / Term D-2017 Problem Se 7 All ex problems from Sedra and Smih, Microelecronic ircuis, 7h ediion. NOTES: Be sure your NAME and

More information

Blast Off! All About SPACE SHUTTLES. All Abou. All About. All Abo. Miriam Gross. ROSEN / PowerKids Press ISBN

Blast Off! All About SPACE SHUTTLES. All Abou. All About. All Abo. Miriam Gross. ROSEN / PowerKids Press ISBN iriam Gross us a n o r s A All Abou s e k c o R u All Abo es i l l e a All Abou s n o i s s i e pac u o b A l Al es l u h e pac u o b A All s n o i a pace u o b A All L T T U H C A P u o b A l l A All

More information

Pointwise Image Operations

Pointwise Image Operations Poinwise Image Operaions Binary Image Analysis Jana Kosecka hp://cs.gmu.edu/~kosecka/cs482.hml - Lookup able mach image inensiy o he displayed brighness values Manipulaion of he lookup able differen Visual

More information

EE 330 Lecture 24. Amplification with Transistor Circuits Small Signal Modelling

EE 330 Lecture 24. Amplification with Transistor Circuits Small Signal Modelling EE 330 Lecure 24 Amplificaion wih Transisor Circuis Small Signal Modelling Review from las ime Area Comparison beween BJT and MOSFET BJT Area = 3600 l 2 n-channel MOSFET Area = 168 l 2 Area Raio = 21:1

More information

Table of Contents. 3.0 SMPS Topologies. For Further Research. 3.1 Basic Components. 3.2 Buck (Step Down) 3.3 Boost (Step Up) 3.4 Inverter (Buck/Boost)

Table of Contents. 3.0 SMPS Topologies. For Further Research. 3.1 Basic Components. 3.2 Buck (Step Down) 3.3 Boost (Step Up) 3.4 Inverter (Buck/Boost) Table of Conens 3.0 SMPS Topologies 3.1 Basic Componens 3.2 Buck (Sep Down) 3.3 Boos (Sep Up) 3.4 nverer (Buck/Boos) 3.5 Flyback Converer 3.6 Curren Boosed Boos 3.7 Curren Boosed Buck 3.8 Forward Converer

More information

Revision: June 11, E Main Suite D Pullman, WA (509) Voice and Fax

Revision: June 11, E Main Suite D Pullman, WA (509) Voice and Fax 2.5.3: Sinusoidal Signals and Complex Exponenials Revision: June 11, 2010 215 E Main Suie D Pullman, W 99163 (509) 334 6306 Voice and Fax Overview Sinusoidal signals and complex exponenials are exremely

More information

EE201 Circuit Theory I Fall

EE201 Circuit Theory I Fall EE1 Circui Theory I 17 Fall 1. Basic Conceps Chaper 1 of Nilsson - 3 Hrs. Inroducion, Curren and Volage, Power and Energy. Basic Laws Chaper &3 of Nilsson - 6 Hrs. Volage and Curren Sources, Ohm s Law,

More information

Transmission Lines. Transmission Lines :: Topics. Introduction Wave Propagation Termination Reflections Summary. Introduction.

Transmission Lines. Transmission Lines :: Topics. Introduction Wave Propagation Termination Reflections Summary. Introduction. Transmission Lines Digial Design and Compuer Archiecure David Money Harris and Sarah L. Harris Transmission Lines :: Topics Inroducion Wave Propagaion Terminaion Reflecions Summary TL- TL- Inroducion

More information

Answer Key for Week 3 Homework = 100 = 140 = 138

Answer Key for Week 3 Homework = 100 = 140 = 138 Econ 110D Fall 2009 K.D. Hoover Answer Key for Week 3 Homework Problem 4.1 a) Laspeyres price index in 2006 = 100 (1 20) + (0.75 20) Laspeyres price index in 2007 = 100 (0.75 20) + (0.5 20) 20 + 15 = 100

More information

Sound so far: 10/13/2013. Sound and stringed instruments

Sound so far: 10/13/2013. Sound and stringed instruments 0/3/203 Sound and ed insrumens Sound so far: Sound is a pressure or densiy flucuaion carried (usually) by air molecules sound wae is longdiudinal Wha is he difference beween a hud and a musical noe? ecure

More information

USING MATLAB TO CREATE AN IMAGE FROM RADAR

USING MATLAB TO CREATE AN IMAGE FROM RADAR USING MATLAB TO CREATE AN IMAGE FROM RADAR Douglas Hulber Mahemaics Deparmen Norfol Sae Universiy 700 Par Avenue Uni 483 Norfol VA 3504-8060 dhulber@nsu.edu Inroducion. Digial imaging algorihms developed

More information

3: Microscopic imaging

3: Microscopic imaging Ouline 3: Microscopic imaging Microscope layou Three limis o resoluion Diracion Pixel size Aberraions Comparison o elescopes and microscopes Rober R. McLeod, Universiy o Colorado 35 Microscope layou Anaomy

More information

Announcement. Allowed

Announcement. Allowed 9//05 nnouncemen Firs es: Sep. 8, Chap. -4 llowed wriing insrumen poce calculaor ruler One 8.5" " paper conaining consans, formulas, and any oher informaion ha you migh find useful (NOT any inds of soluions).

More information

Explanation of Maximum Ratings and Characteristics for Thyristors

Explanation of Maximum Ratings and Characteristics for Thyristors 8 Explanaion of Maximum Raings and Characerisics for Thyrisors Inroducion Daa shees for s and riacs give vial informaion regarding maximum raings and characerisics of hyrisors. If he maximum raings of

More information

Institutional Assessment Report Texas Southern University College of Pharmacy and Health Sciences "P1-Entering Class Fall 2013

Institutional Assessment Report Texas Southern University College of Pharmacy and Health Sciences P1-Entering Class Fall 2013 Insiuional Assessmen Repor Texas Souhern Universiy College of Pharmacy and Healh Sciences "P1-Enering Class Fall 2013 Correlaions Fall 2013 GPA Calculaions PODA I To. Ps. To. Ps. (PHAR (PHAR-438) 433)

More information

5 Spatial Relations on Lines

5 Spatial Relations on Lines 5 Spaial Relaions on Lines There are number of useful problems ha can be solved wih he basic consrucion echniques developed hus far. We now look a cerain problems, which involve spaial relaionships beween

More information

English (Standard) and English (Advanced)

English (Standard) and English (Advanced) 2004 HIGHER SCHOOL CERTIFICATE EXAMINATION English (Sandard) and English (Advanced) Paper 1 Area of Sudy Toal marks 45 Secion I Pages 2 7 General Insrucions Reading ime 10 minues Working ime 2 hours Wrie

More information

10. The Series Resistor and Inductor Circuit

10. The Series Resistor and Inductor Circuit Elecronicsab.nb 1. he Series esisor and Inducor Circui Inroducion he las laboraory involved a resisor, and capacior, C in series wih a baery swich on or off. I was simpler, as a pracical maer, o replace

More information

THE OSCILLOSCOPE AND NOISE. Objectives:

THE OSCILLOSCOPE AND NOISE. Objectives: -26- Preparaory Quesions. Go o he Web page hp://www.ek.com/measuremen/app_noes/xyzs/ and read a leas he firs four subsecions of he secion on Trigger Conrols (which iself is a subsecion of he secion The

More information

Multipath. Introduction. Theory. Multipath 7.1

Multipath. Introduction. Theory. Multipath 7.1 Mulipa 7. Mulipa Inroducion Tere are wo caracerisics o radio cannels a presen serious diiculies or elecommunicaion sysems. One is e remendous dynamic range a mus be accommodaed due o e large cange in pa

More information

Lecture September 6, 2011

Lecture September 6, 2011 cs294-p29 Seminar on Algorihmic Game heory Sepember 6, 2011 Lecure Sepember 6, 2011 Lecurer: Chrisos H. Papadimiriou Scribes: Aloni Cohen and James Andrews 1 Game Represenaion 1.1 abular Form and he Problem

More information

RANCH RAIL FENCE AND GATE INSTALLATION INSTRUCTIONS

RANCH RAIL FENCE AND GATE INSTALLATION INSTRUCTIONS Good Fences Make Good Neighbors RANCH RAIL FENCE AND GATE INSTALLATION INSTRUCTIONS HUSKER VINYL Ranch Rail Fence & Gae Insallaion Insrucions 1 BEFORE YOU START, IT S IMPORTANT TO CHECK: Tha fence or he

More information

Installation and Operating Instructions for ROBA -brake-checker Typ

Installation and Operating Instructions for ROBA -brake-checker Typ (B.018102.EN) Guidelines on he Declaraion of Conformiy A conformiy evaluaion has been carried ou for he produc in erms of he EC Low Volage Direcive 2006/95/ EC and EMC Direcive 2004/108/EC. The Declaraion

More information

Errata and Updates for ASM Exam MLC (Fourteenth Edition) Sorted by Page

Errata and Updates for ASM Exam MLC (Fourteenth Edition) Sorted by Page Erraa for ASM Exam MLC Sudy Manual (Foureenh Ediion) Sored by Page 1 Erraa and Updaes for ASM Exam MLC (Foureenh Ediion) Sored by Page Pracice Exam 7:25 (page 1386) is defecive, Pracice Exam 5:21 (page

More information

UNIT IV DIGITAL MODULATION SCHEME

UNIT IV DIGITAL MODULATION SCHEME UNI IV DIGIAL MODULAION SCHEME Geomeric Represenaion of Signals Ojecive: o represen any se of M energy signals {s i (} as linear cominaions of N orhogonal asis funcions, where N M Real value energy signals

More information

Comparing image compression predictors using fractal dimension

Comparing image compression predictors using fractal dimension Comparing image compression predicors using fracal dimension RADU DOBRESCU, MAEI DOBRESCU, SEFA MOCAU, SEBASIA ARALUGA Faculy of Conrol & Compuers POLIEHICA Universiy of Buchares Splaiul Independenei 313

More information

READING ASSIGNMENTS LECTURE OBJECTIVES. Problem Solving Skills. x(t) = cos(αt 2 ) ELEG-212 Signal Processing and Communications

READING ASSIGNMENTS LECTURE OBJECTIVES. Problem Solving Skills. x(t) = cos(αt 2 ) ELEG-212 Signal Processing and Communications ELEG- Signal Processing and Communicaions Lecure 5 Periodic Signals, Harmonics & ime-varying Sinusoids READING ASSIGNMENS his Lecure: Chaper 3, Secions 3- and 3-3 Chaper 3, Secions 3-7 and 3-8 Lab sars

More information

Volume Author/Editor: Simon Kuznets, assisted by Elizabeth Jenks. Volume URL:

Volume Author/Editor: Simon Kuznets, assisted by Elizabeth Jenks. Volume URL: This PDF is a selecion from an ou-of-prin volume from he Naional Bureau of Economic Research Volume Tile: Shares of Upper Income Groups in Income and Savings Volume Auhor/Edior: Simon Kuznes, assised by

More information

Square Waves, Sinusoids and Gaussian White Noise: A Matching Pursuit Conundrum? Don Percival

Square Waves, Sinusoids and Gaussian White Noise: A Matching Pursuit Conundrum? Don Percival Square Waves, Sinusoids and Gaussian Whie Noise: A Maching Pursui Conundrum? Don Percival Applied Physics Laboraory Deparmen of Saisics Universiy of Washingon Seale, Washingon, USA hp://faculy.washingon.edu/dbp

More information

Experiment 6: Transmission Line Pulse Response

Experiment 6: Transmission Line Pulse Response Eperimen 6: Transmission Line Pulse Response Lossless Disribued Neworks When he ime required for a pulse signal o raverse a circui is on he order of he rise or fall ime of he pulse, i is no longer possible

More information

An off-line multiprocessor real-time scheduling algorithm to reduce static energy consumption

An off-line multiprocessor real-time scheduling algorithm to reduce static energy consumption An off-line muliprocessor real-ime scheduling algorihm o reduce saic energy consumpion Firs Workshop on Highly-Reliable Power-Efficien Embedded Designs Shenzhen, China Vincen Legou, Mahieu Jan, Lauren

More information

EXPERIMENT #9 FIBER OPTIC COMMUNICATIONS LINK

EXPERIMENT #9 FIBER OPTIC COMMUNICATIONS LINK EXPERIMENT #9 FIBER OPTIC COMMUNICATIONS LINK INTRODUCTION: Much of daa communicaions is concerned wih sending digial informaion hrough sysems ha normally only pass analog signals. A elephone line is such

More information

Spring Localization I. Roland Siegwart, Margarita Chli, Martin Rufli. ASL Autonomous Systems Lab. Autonomous Mobile Robots

Spring Localization I. Roland Siegwart, Margarita Chli, Martin Rufli. ASL Autonomous Systems Lab. Autonomous Mobile Robots Spring 2017 Localizaion I Localizaion I 10.04.2017 1 2 ASL Auonomous Sysems Lab knowledge, daa base mission commands Localizaion Map Building environmen model local map posiion global map Cogniion Pah

More information

Synchronization of single-channel stepper motor drivers reduces noise and interference

Synchronization of single-channel stepper motor drivers reduces noise and interference hronizaion of single-channel sepper moor drivers reduces noise and inerference n mos applicaions, a non-synchronized operaion causes no problems. However, in some cases he swiching of he wo channels inerfere,

More information

Parametrizations of curves on a plane (Sect. 11.1)

Parametrizations of curves on a plane (Sect. 11.1) Paramerizaions of curves on a plane (Sec..) Review: Curves on he plane. Parameric equaions of a curve. s of curves on he plane. The ccloid. Review: Curves on he plane Remarks: Curves on a plane can be

More information

Attitude Estimation of A Rocking Ship with The Angle of Arrival Measurements Using Beacons

Attitude Estimation of A Rocking Ship with The Angle of Arrival Measurements Using Beacons IOSR Journal of VLSI and Signal Processing (IOSR-JVSP) Volume 6, Issue 5, Ver. I (Sep. - Oc. 2016), PP 60-66 e-issn: 2319 4200, p-issn No. : 2319 4197 www.iosrjournals.org Aiude Esimaion of A Rocing Ship

More information

EXPERIMENT #4 AM MODULATOR AND POWER AMPLIFIER

EXPERIMENT #4 AM MODULATOR AND POWER AMPLIFIER EXPERIMENT #4 AM MODULATOR AND POWER AMPLIFIER INTRODUCTION: Being able o ransmi a radio frequency carrier across space is of no use unless we can place informaion or inelligence upon i. This las ransmier

More information

TELE4652 Mobile and Satellite Communications

TELE4652 Mobile and Satellite Communications TELE465 Mobile and Saellie Communicaions Assignmen (Due: 4pm, Monday 7 h Ocober) To be submied o he lecurer before he beginning of he final lecure o be held a his ime.. This quesion considers Minimum Shif

More information

f t 2cos 2 Modulator Figure 21: DSB-SC modulation.

f t 2cos 2 Modulator Figure 21: DSB-SC modulation. 4.5 Ampliude modulaion: AM 4.55. DSB-SC ampliude modulaion (which is summarized in Figure 21) is easy o undersand and analyze in boh ime and frequency domains. However, analyical simpliciy is no always

More information

= f 8 f 2 L C. i C. 8 f C. Q1 open Q2 close (1+D)T DT 2. i C = i L. Figure 2: Typical Waveforms of a Step-Down Converter.

= f 8 f 2 L C. i C. 8 f C. Q1 open Q2 close (1+D)T DT 2. i C = i L. Figure 2: Typical Waveforms of a Step-Down Converter. Inroducion Oupu Volage ipple in Sep-Down and Sep-Up Swiching egulaors Oupu volage ripple is always an imporan performance parameer wih DC-DC converers. For inducor-based swiching regulaors, several key

More information

Social-aware Dynamic Router Node Placement in Wireless Mesh Networks

Social-aware Dynamic Router Node Placement in Wireless Mesh Networks Social-aware Dynamic Rouer Node Placemen in Wireless Mesh Neworks Chun-Cheng Lin Pei-Tsung Tseng Ting-Yu Wu Der-Jiunn Deng ** Absrac The problem of dynamic rouer node placemen (dynrnp) in wireless mesh

More information

Automatic Power Factor Control Using Pic Microcontroller

Automatic Power Factor Control Using Pic Microcontroller IDL - Inernaional Digial Library Of Available a:www.dbpublicaions.org 8 h Naional Conference on Advanced Techniques in Elecrical and Elecronics Engineering Inernaional e-journal For Technology And Research-2017

More information

Examination Mobile & Wireless Networking ( ) April 12,

Examination Mobile & Wireless Networking ( ) April 12, Page 1 of 5 Examinaion Mobile & Wireless Neworking (192620010) April 12, 2017 13.45 16.45 Noes: Only he overhead shees used in he course, 2 double-sided shees of noes (any fon size/densiy!), and a dicionary

More information

Signal Characteristics

Signal Characteristics Signal Characerisics Analog Signals Analog signals are always coninuous (here are no ime gaps). The signal is of infinie resoluion. Discree Time Signals SignalCharacerisics.docx 8/28/08 10:41 AM Page 1

More information

ISSCC 2007 / SESSION 29 / ANALOG AND POWER MANAGEMENT TECHNIQUES / 29.8

ISSCC 2007 / SESSION 29 / ANALOG AND POWER MANAGEMENT TECHNIQUES / 29.8 ISSCC 27 / SESSION 29 / ANALOG AND POWER MANAGEMENT TECHNIQUES / 29.8 29.8 A 3GHz Swiching DC-DC Converer Using Clock- Tree Charge-Recycling in 9nm CMOS wih Inegraed Oupu Filer Mehdi Alimadadi, Samad Sheikhaei,

More information

MAP-AIDED POSITIONING SYSTEM

MAP-AIDED POSITIONING SYSTEM Paper Code: F02I131 MAP-AIDED POSITIONING SYSTEM Forssell, Urban 1 Hall, Peer 1 Ahlqvis, Sefan 1 Gusafsson, Fredrik 2 1 NIRA Dynamics AB, Sweden; 2 Linköpings universie, Sweden Keywords Posiioning; Navigaion;

More information

March 13, 2009 CHAPTER 3: PARTIAL DERIVATIVES AND DIFFERENTIATION

March 13, 2009 CHAPTER 3: PARTIAL DERIVATIVES AND DIFFERENTIATION March 13, 2009 CHAPTER 3: PARTIAL DERIVATIVES AND DIFFERENTIATION 1. Parial Derivaives and Differeniable funcions In all his chaper, D will denoe an open subse of R n. Definiion 1.1. Consider a funcion

More information

OpenStax-CNX module: m Elemental Signals. Don Johnson. Perhaps the most common real-valued signal is the sinusoid.

OpenStax-CNX module: m Elemental Signals. Don Johnson. Perhaps the most common real-valued signal is the sinusoid. OpenSax-CNX module: m0004 Elemenal Signals Don Johnson This work is produced by OpenSax-CNX and licensed under he Creaive Commons Aribuion License.0 Absrac Complex signals can be buil from elemenal signals,

More information

Computer Graphic with Matrices Math 308A Project

Computer Graphic with Matrices Math 308A Project Compue Gaphic wih Maices Mah 38A Pojec Suden: Wei-Liang Chen Suden #: 3292 Dae: Dec 3 d, 2 Pofesso: James King Imagine ha ou ae dawing a picue b hand o compue. The picue we daw b compue ae called compue

More information

Role of Kalman Filters in Probabilistic Algorithm

Role of Kalman Filters in Probabilistic Algorithm Volume 118 No. 11 2018, 5-10 ISSN: 1311-8080 (prined version); ISSN: 1314-3395 (on-line version) url: hp://www.ijpam.eu doi: 10.12732/ijpam.v118i11.2 ijpam.eu Role of Kalman Filers in Probabilisic Algorihm

More information

Laplacian Mixture Modeling for Overcomplete Mixing Matrix in Wavelet Packet Domain by Adaptive EM-type Algorithm and Comparisons

Laplacian Mixture Modeling for Overcomplete Mixing Matrix in Wavelet Packet Domain by Adaptive EM-type Algorithm and Comparisons Proceedings of he 5h WSEAS Inernaional Conference on Signal Processing, Isanbul, urey, May 7-9, 6 (pp45-5) Laplacian Mixure Modeling for Overcomplee Mixing Marix in Wavele Pace Domain by Adapive EM-ype

More information

Simulation Series Termination

Simulation Series Termination ESE370: Circui-Level Modeling, Design, and Opimizaion for Digial Sysems Day 35: December 5, 2012 Transmission Lines Implicaions 1 Transmission Line Agenda Where arise? General wire formulaion Lossless

More information

Development and Validation of Flat-Plate Collector Testing Procedures

Development and Validation of Flat-Plate Collector Testing Procedures Developmen and Validaion of Fla-Plae Collecor Tesing Procedures Repor for November, 2006 Focus on Energy (FOE) suppors solar hermal sysems ha displace convenional fuels by offering cash-back rebaes ha

More information

Network Performance Metrics

Network Performance Metrics Fundamenals of Compuer Neworks ECE 478/578 Lecure #3 Insrucor: Loukas Lazos Dep of Elecrical and Compuer Engineering Universiy of rizona Nework Performance Merics andwidh moun of daa ransmied per uni of

More information

ECE ANALOG COMMUNICATIONS - INVESTIGATION 7 INTRODUCTION TO AMPLITUDE MODULATION - PART II

ECE ANALOG COMMUNICATIONS - INVESTIGATION 7 INTRODUCTION TO AMPLITUDE MODULATION - PART II ECE 405 - ANALOG COMMUNICATIONS - INVESTIGATION 7 INTRODUCTION TO AMPLITUDE MODULATION - PART II FALL 2005 A.P. FELZER To do "well" on his invesigaion you mus no only ge he righ answers bu mus also do

More information

Figure A linear pair? Explain. No, because vertical angles are not adjacent angles, and linear pairs are.

Figure A linear pair? Explain. No, because vertical angles are not adjacent angles, and linear pairs are. Geomery Review of PIL KEY Name: Parallel and Inersecing Lines Dae: Per.: PIL01: Use complemenary supplemenary and congruen o compare wo angles. 1) Complee he following definiion: Two angles are Complemenary

More information

GaN-HEMT Dynamic ON-state Resistance characterisation and Modelling

GaN-HEMT Dynamic ON-state Resistance characterisation and Modelling GaN-HEMT Dynamic ON-sae Resisance characerisaion and Modelling Ke Li, Paul Evans, Mark Johnson Power Elecronics, Machine and Conrol group Universiy of Noingham, UK Email: ke.li@noingham.ac.uk, paul.evans@noingham.ac.uk,

More information

Deblurring Images via Partial Differential Equations

Deblurring Images via Partial Differential Equations Deblurring Images via Parial Dierenial Equaions Sirisha L. Kala Mississippi Sae Universiy slk3@mssae.edu Advisor: Seh F. Oppenheimer Absrac: Image deblurring is one o he undamenal problems in he ield o

More information

Estimating a Time-Varying Phillips Curve for South Africa

Estimating a Time-Varying Phillips Curve for South Africa Esimaing a Time-Varying Phillips Curve for Souh Africa Alain Kabundi* 1 Eric Schaling** Modese Some*** *Souh African Reserve Bank ** Wis Business School and VU Universiy Amserdam *** World Bank 27 Ocober

More information

A WIDEBAND RADIO CHANNEL MODEL FOR SIMULATION OF CHAOTIC COMMUNICATION SYSTEMS

A WIDEBAND RADIO CHANNEL MODEL FOR SIMULATION OF CHAOTIC COMMUNICATION SYSTEMS A WIDEBAND RADIO CHANNEL MODEL FOR SIMULATION OF CHAOTIC COMMUNICATION SYSTEMS Kalle Rui, Mauri Honanen, Michael Hall, Timo Korhonen, Veio Porra Insiue of Radio Communicaions, Helsini Universiy of Technology

More information

When answering the following 25 questions, always remember that there is someone who has to grade them. So please use legible handwriting.

When answering the following 25 questions, always remember that there is someone who has to grade them. So please use legible handwriting. 38963, VU Mobile Kommunikaion Miderm Exam: Insiu für Nachrichenechnik und Hochfrequenzechnik When answering he following 5 quesions, always remember ha here is someone who has o grade hem So please use

More information

Passband Data Transmission II References Frequency-shift keying Chapter 6.5, S. Haykin, Communication Systems, Wiley. H.1

Passband Data Transmission II References Frequency-shift keying Chapter 6.5, S. Haykin, Communication Systems, Wiley. H.1 Passand Daa ransmission II Reerences Frequency-shi keying Chaper 6.5, S. Haykin, Communicaion Sysems, Wiley. H. Inroducion Inroducion PSK and QAM are linear modulaion FSK is a nonlinear modulaion Similar

More information

Chapter 2 Introduction: From Phase-Locked Loop to Costas Loop

Chapter 2 Introduction: From Phase-Locked Loop to Costas Loop Chaper 2 Inroducion: From Phase-Locked Loop o Cosas Loop The Cosas loop can be considered an exended version of he phase-locked loop (PLL). The PLL has been invened in 932 by French engineer Henri de Belleszice

More information

Direct Analysis of Wave Digital Network of Microstrip Structure with Step Discontinuities

Direct Analysis of Wave Digital Network of Microstrip Structure with Step Discontinuities Direc Analysis of Wave Digial Nework of Microsrip Srucure wih Sep Disconinuiies BILJANA P. SOŠIĆ Faculy of Elecronic Engineering Universiy of Niš Aleksandra Medvedeva 4, Niš SERBIA MIODRAG V. GMIROVIĆ

More information

Driver Modeling and Alignment for Worst-Case Delay Noise

Driver Modeling and Alignment for Worst-Case Delay Noise Drier Modeling and Alignmen for Wors-Case Noise Supamas Sirichoiyakul, Daid Blaauw, Chanhee Oh, Rafi Ley*, Vladimir Zoloo, Jingyan Zuo Moorola Inc. Ausin, TX, *Moorola Semiconducor Israel Ld. Tel Ai, Israel

More information

A Simplified Approach to Understanding the Kalman Filter Technique

A Simplified Approach to Understanding the Kalman Filter Technique Universiy of Richmond UR Scholarship Reposiory Finance Faculy Publicaions Finance 008 A Simplified Approach o Undersanding he Kalman Filer Technique Tom Arnold Universiy of Richmond, arnold@richmond.edu

More information

Laboratory #2. Spectral Analysis of Digital Baseband Signals. SYSC 4600 Digital Communications

Laboratory #2. Spectral Analysis of Digital Baseband Signals. SYSC 4600 Digital Communications Laboraory #2 Speral Analysis of Digial Baseband Signals SYSC 4600 Digial Communiaions Deparmen of Sysems and Compuer Engineering Fauly of Engineering Carleon Universiy Oober 206 Deparmen of Sysems & Compuer

More information

B-MAC Tunable MAC protocol for wireless networks

B-MAC Tunable MAC protocol for wireless networks B-MAC Tunable MAC proocol for wireless neworks Summary of paper Versaile Low Power Media Access for Wireless Sensor Neworks Presened by Kyle Heah Ouline Inroducion o B-MAC Design of B-MAC B-MAC componens

More information

SLAM Algorithm for 2D Object Trajectory Tracking based on RFID Passive Tags

SLAM Algorithm for 2D Object Trajectory Tracking based on RFID Passive Tags 2008 IEEE Inernaional Conference on RFID The Veneian, Las Vegas, Nevada, USA April 16-17, 2008 1C2.2 SLAM Algorihm for 2D Objec Trajecory Tracking based on RFID Passive Tags Po Yang, Wenyan Wu, Mansour

More information

OPERATION MANUAL. Indoor unit for air to water heat pump system and options EKHBRD011AAV1 EKHBRD014AAV1 EKHBRD016AAV1

OPERATION MANUAL. Indoor unit for air to water heat pump system and options EKHBRD011AAV1 EKHBRD014AAV1 EKHBRD016AAV1 OPERAION MANUAL Indoor uni for air o waer hea pump sysem and opions EKHBRD011AAV1 EKHBRD014AAV1 EKHBRD016AAV1 EKHBRD011AAY1 EKHBRD014AAY1 EKHBRD016AAY1 EKHBRD011AAV1 EKHBRD014AAV1 EKHBRD016AAV1 EKHBRD011AAY1

More information

Universal microprocessor-based ON/OFF and P programmable controller MS8122A MS8122B

Universal microprocessor-based ON/OFF and P programmable controller MS8122A MS8122B COMPETENCE IN MEASUREMENT Universal microprocessor-based ON/OFF and P programmable conroller MS8122A MS8122B TECHNICAL DESCRIPTION AND INSTRUCTION FOR USE PLOVDIV 2003 1 I. TECHNICAL DATA Analog inpus

More information

Evaluation of Instantaneous Reliability Measures for a Gradual Deteriorating System

Evaluation of Instantaneous Reliability Measures for a Gradual Deteriorating System General Leers in Mahemaic, Vol. 3, No.3, Dec 27, pp. 77-85 e-issn 259-9277, p-issn 259-9269 Available online a hp:\\ www.refaad.com Evaluaion of Insananeous Reliabiliy Measures for a Gradual Deerioraing

More information

Installing remote sites using TCP/IP

Installing remote sites using TCP/IP v dc Keypad from nework Whie/ 3 Whie/ 4 v dc Keypad from nework Whie/ 3 Whie/ 4 v dc Keypad from nework Whie/ 3 Whie/ 4 +v pu +v pu +v pu v dc Keypad from nework Whie/ 3 Whie/ 4 v dc Keypad from nework

More information

2.6 Special Angles on Parallel Lines Objectives: I CAN define angle pairs made by parallel lines. I CAN solve problems involving parallel lines.

2.6 Special Angles on Parallel Lines Objectives: I CAN define angle pairs made by parallel lines. I CAN solve problems involving parallel lines. 2.6 Special Angles on Parallel Lines Objecives: I CAN define angle pairs made by parallel lines. I CAN solve problems involving parallel lines. 1 coplanar: poins on he same plane ransversal: a line ha

More information

OPERATION MANUAL. Indoor unit for air to water heat pump system and options EKHBRD011ADV1 EKHBRD014ADV1 EKHBRD016ADV1

OPERATION MANUAL. Indoor unit for air to water heat pump system and options EKHBRD011ADV1 EKHBRD014ADV1 EKHBRD016ADV1 OPERAION MANUAL Indoor uni for air o waer hea pump sysem and opions EKHBRD011ADV1 EKHBRD014ADV1 EKHBRD016ADV1 EKHBRD011ADY1 EKHBRD014ADY1 EKHBRD016ADY1 EKHBRD011ADV1+Y1 EKHBRD014ADV1+Y1 EKHBRD016ADV1+Y1

More information

Calculation on the Inter-Lobe Clearance Distribution of Twin-Screw Compressor by Optimization Method

Calculation on the Inter-Lobe Clearance Distribution of Twin-Screw Compressor by Optimization Method Purdue Universi Purdue e-pubs Inernaional Compressor Engineering Conference School of echanical Engineering 6 Calculaion on he Iner-Lobe Clearance Disribuion of Twin-Screw Compressor b Opimiaion ehod Wei

More information

Investigation and Simulation Model Results of High Density Wireless Power Harvesting and Transfer Method

Investigation and Simulation Model Results of High Density Wireless Power Harvesting and Transfer Method Invesigaion and Simulaion Model Resuls of High Densiy Wireless Power Harvesing and Transfer Mehod Jaber A. Abu Qahouq, Senior Member, IEEE, and Zhigang Dang The Universiy of Alabama Deparmen of Elecrical

More information