Energizing Math with Engineering Applications
|
|
- Britney Spencer
- 5 years ago
- Views:
Transcription
1 Enerizin Math with Enineerin Applications Understandin the Math behind Launchin a Straw-Rocket throuh the use of Simulations. Activity created by Ira Rosenthal (rosenthi@palmbeachstate.edu) as part of the NSF-funded InnovATE rant. Presented at the Back to School Math Conference Santaluces Hih School Auust 8, 016
2 An application of Projectile Motion: Launchin a Rocket (or a Baseball or a Golf Ball etc ) Learnin Outcomes: Upon completin this activity, students will be able to: Understand the relationship between a mathematical formula and what it represents in real life. Investiate relationships between two variables throuh the creation of a scatter plot and throuh the analysis of the equation that relates the variables. Solve a iven formula for one of the variables, in order to make a projectile hit a preset taret. Terminoloy: The distance traveled horizontally from the launch position to the landin position is known as the rane, shown as R in the iven fiure. The maximum heiht reached by the projectile is shown as H, and the launch anle is marked as θ. The initial velocity of the projectile is represented as Vo. For all of the followin questions, we will assume that the initial heiht is 0, that is the object is bein thrown from the round level. Use a rocket launcher or a simulation website such as the one found in to answer the followin questions. 1) Initial Guess: How do you think the rane of the projectile will chane as the anle chanes (assumin a fixed initial velocity)? How do you think the rane will chane as the initial velocity chanes (assumin a fixed anle)? How do you think the maximum vertical distance from the round will chane as the anle chanes (assumin a fixed initial velocity)? 1
3 ) Experimentation and Data Collection: Please note that you won t be able to use the values iven at the top of the simulator, since the projectile in that simulation is not thrown from (0,0) level. Instead use the tape measure to determine the rane and the maximum heiht. Measure from and to the ray horizontal line, as this represents the level from which the object is launched. For the rane, the tape measure should be set so the plus sin is alined with the plus sin of the canon s wheel (at the (0,0) position), since we will assume that this represents the startin point of the ball s trajectory. So, for example, select olf ball option, enter 65 for the anle, and 10 for the initial speed. Click on Fire. When the path of the olf ball is displayed, use the tape measurement tool to measure the distance between the startin point (oriin) and the point where the object landed on the x-axis. You should be able to et about 7.8m. Place this value in the table below, and repeat this for the rest of the values iven. A) Projectile Launch Anle versus Rane (for a fixed initial velocity): First, you will investiate how the launch anle impacts the rane of the projectile. For this question, use a fixed initial velocity, such as 10 m/s, and vary the anle. After each trial, measure the rane and record it below. Then, create a scatter plot of the points obtained in the table. Make sure to label the axes of the raph and choose an appropriate scale. Launch anle (derees) =10m/s Rane (m)
4 Conclusion: Describe how the launch anle and rane are related, makin sure to comment on which anle results in maximum rane. Also comment on if this conclusion arees with your initial uess. B) Initial Velocity versus Rane of the Projectile (for a fixed anle): For this exercise, you will investiate how the initial velocity impacts the rane of the olf ball. Use a fixed anle of 45 derees, and vary the initial velocity as suested below. Fill in the followin table usin the simulator, and then raph the results in the coordinate system provided. Make sure to label the axes and choose an appropriate scale for the axes. Notes: Clear the previous trials by clickin on erase prior to startin this portion. Also, note that you can zoom in or out by clickin on the + or - sins located riht above the fire command. This will help you measure distances more accurately. θ = 45 Initial Velocity(m/s) Rane Conclusion: (For a fixed anle) As the initial velocity increases, the rane Does initial velocity and rane appear to have a linear or quadratic relationship? How can we tell? 3
5 C) Launch Anle versus Maximum Heiht Reached (for a fixed initial velocity) For this question, you will investiate how the launch anle affects the maximum heiht reached. Assume a fixed initial velocity, such as 15 m/s. =15 m/s Launch Anle derees) Maximum heiht (m) Conclusion: Describe how the launch anle and maximum heiht are related: 3) Checkin the Experimental Results aainst the Theoretical Formulas: A formula from physics relates ives the rane of a projectile as a function of the launch anle and the initial velocity. R sin( ) and θ represents the launch anle in derees. θ = where = 9.8 m/s, is the initial velocity (m/s) A) Launch Anle vs. Rane: In (A) above, you created a table usin empirical data on the relationship between the anle of the projectile and the rane. Let s check one of those values usin the formula. For θ =45 derees, and once aain assumin that =10 m/s, what does the formula ive for the value of R? (Make sure your calculator is in deree mode.) Show work in the space provided. How does this compare this with the value obtained in (A) for a 45 deree launch? R = sin( θ ) 4
6 B) Initial Velocity vs. Rane: In (B) above, you explored the relationship between initial velocity and rane of the projectile. Now, use the formula iven above to check the case where initial velocity equals 0 m/s. Recall that for this part, we used a fixed anle of 45 derees for each of the trials. How does the formula prediction for R compare with the experimental results? R = sin( θ ) Take a look at the above formula once aain. For a fixed anle, this formula would ive the rane as a function of the initial velocity. Does this formula confirm your conclusions about whether the relationship between the variables is linear or quadratic? Explain. C) Launch Anle versus Maximum Heiht: The formula from physics that relates these two variables is iven on the riht: Use this formula to check one of the entries (θ =40 de.) from your table in (C) above. Recall that we had assumed = 15 m/s for that part. How does the answer obtained from the formula compare with the answer obtained from the experiment (or simulation) in C? H V0 sin = θ Explain, investiatin the above formula, why the hihest value of the maximum heiht is attained with an initial anle of 90 derees. 5
7 4) Settin the Correct Parameters in Order to Hit a Taret A) In order to hit a taret that is 18 m from the canon, and usin an initial velocity of 0 m/s, what launch anle should be used? Start by measurin a distance that is 18 m from the initial point, and dra the taret there. First use trial-and-error by adjustin the simulator launch anle to et a rouh estimate for the anle that will do the job. Don t waste too much time here, since you will be able to find the exact anle in the next part. Estimated anle: Next, use the followin formula to determine the anle of the projectile that will result in hittin the taret. (= 9.8m/s, represents the initial velocity and R is the rane. Since the unknown is θ, you will need to solve this equation for θ.) R = sin( θ ) B) Determine the initial velocity that one needs to hit a olf ball in order to hit a taret that is 60m away from the initial position. For this question, assume that the anle is 45 derees. You can use the formula introduced above, and check your answer usin the simulator. C) Use the maximum heiht formula to determine the initial velocity for launchin the olf ball, so that the maximum heiht that it reaches equals 5. meters, assumin that the launch anle is 30 derees. Use the iven formula to determine the answer, and then check your answer usin the simulation. To check the answer, you will need to place a taret 5. m. above the x- axis- but where should this taret be placed horizontally? H V0 sin θ = 6
8 5) Derivation of Some of the Formulas Used: Two main equations for projectile motion are the equations that describe the vertical and the horizontal components of motion. 1 Vertical motion: y = t + V0sin( θ ) t+ y0, where y represents distance from the round t seconds after the projectile was thrown in the air. (For this question y 0 = 0, since initial distance from the round is assumed to be 0.) Horizontal motion: x = V cos( θ ) t 0, where x represents the horizontal distance from the initial point, t seconds after it was launched. A) Determine the time to reach maximum heiht usin the first equation above. Hint: the maximum heiht for a parabola is reached at t = - b/(a), where a is the coef. of the quadratic term, and b is the coef. of the linear term. [Students who have taken calculus can find the maximum by settin dy/dt =0] B) Use your answer from (A) above to derive the formula: H V0 sin θ =, which ives the maximum heiht reached by the projectile. [Basically, all you need to do is to substitute the value of time found above into the vertical motion equation, to find the heiht at that moment in time.] C) Derive the rane formula iven below. To find an equation that ives the rane as a function of initial velocity and the anle theta, you will use the fact that when the object reaches the round, y =0. That will ive us one equation, where you can solve for t. Also, when the object reaches the round, x=r. This will ive you a second equation, where you can also solve for t. Basically, both t s are equal since they both represent total fliht time of the projectile from start to when it hits the round So, set the two t equations equal and solve for R. You will also need to know the double anle formula: sin( θ) = sinθcosθ sin( θ ) R = 7
Projectile Motion. Equipment: Ballistic Gun Apparatus Projectiles Table Clamps 2-meter Stick Carbon Paper, Scratch Paper, Masking Tape Plumb Bob
Purpose: To calculate the initial speed of a projectile by measurin its rane. To predict how far a projectile will travel when fired at different anles, and test these predictions. To predict what anle
More informationv( t) g 2 v 0 sin θ ( ) ( ) g t ( ) = 0
PROJECTILE MOTION Velocity We seek to explore the velocity of the projectile, includin its final value as it hits the round, or a taret above the round. The anle made by the velocity vector with the local
More informationFiring an Ideal Projectile
92 Chapter 13: Vector-Valued Functions and Motion in Space 13.2 Modelin Projectile Motion 921 r at time t v v cos i a j (a) v sin j Newton s second law of motion sas that the force actin on the projectile
More informationPSI AP Physics C Kinematics 2D. Multiple Choice Questions
PSI AP Physics C Kinematics D Multiple Choice Questions 1. A tennis ball is thrown off a cliff 10 m above the round with an initial horizontal velocity of 5 m/s as shown above. The time between the ball
More information2.2 Differentiation and Integration of Vector-Valued Functions
.. DIFFERENTIATION AND INTEGRATION OF VECTOR-VALUED FUNCTIONS133. Differentiation and Interation of Vector-Valued Functions Simply put, we differentiate and interate vector functions by differentiatin
More informationProblem Set 2 Solutions
UNIVERSITY OF ALABAMA Department of Physics and Astronomy PH 125 / LeClair Sprin 2009 Problem Set 2 Solutions The followin three problems are due 20 January 2009 at the beinnin of class. 1. (H,R,&W 4.39)
More informationParametric Equations
Parametric Equations Suppose a cricket jumps off of the round with an initial velocity v 0 at an anle θ. If we take his initial position as the oriin, his horizontal and vertical positions follow the equations:
More informationGet Solution of These Packages & Learn by Video Tutorials on PROJECTILE MOTION
FREE Download Study Packae from website: www.tekoclasses.com & www.mathsbysuha.com Get Solution of These Packaes & Learn by Video Tutorials on www.mathsbysuha.com. BASIC CONCEPT :. PROJECTILE PROJECTILE
More informationPHY 133 Lab 1 - The Pendulum
3/20/2017 PHY 133 Lab 1 The Pendulum [Stony Brook Physics Laboratory Manuals] Stony Brook Physics Laboratory Manuals PHY 133 Lab 1 - The Pendulum The purpose of this lab is to measure the period of a simple
More informationXI PHYSICS M. AFFAN KHAN LECTURER PHYSICS, AKHSS, K. https://promotephysics.wordpress.com
XI PHYSICS M. AFFAN KHAN LECTURER PHYSICS, AKHSS, K affan_414@live.com https://promotephysics.wordpress.com [MOTION IN TWO DIMENSIONS] CHAPTER NO. 4 In this chapter we are oin to discuss motion in projectile
More informationthe equations for the motion of the particle are written as
Dynamics 4600:203 Homework 02 Due: ebruary 01, 2008 Name: Please denote your answers clearly, ie, box in, star, etc, and write neatly There are no points for small, messy, unreadable work please use lots
More informationProblem Set: Fall #1 - Solutions
Problem Set: Fall #1 - Solutions 1. (a) The car stops speedin up in the neative direction and beins deceleratin, probably brakin. (b) Calculate the averae velocity over each time interval. v av0 v 0 +
More information(C) 7 s. (C) 13 s. (C) 10 m
NAME: Ms. Dwarka, Principal Period: #: WC Bryant HS Ms. Simonds, AP Science Base your answers to questions 1 throuh 3 on the position versus time raph below which shows the motion of a particle on a straiht
More information(a) 1m s -2 (b) 2 m s -2 (c) zero (d) -1 m s -2
11 th Physics - Unit 2 Kinematics Solutions for the Textbook Problems One Marks 1. Which one of the followin Cartesian coordinate system is not followed in physics? 5. If a particle has neative velocity
More information1 CHAPTER 7 PROJECTILES. 7.1 No Air Resistance
CHAPTER 7 PROJECTILES 7 No Air Resistance We suppose that a particle is projected from a point O at the oriin of a coordinate system, the y-axis bein vertical and the x-axis directed alon the round The
More informationKINEMATICS PREVIOUS EAMCET BITS ENGINEERING PAPER
KINEMATICS PREVIOUS EAMCET BITS ENGINEERING PAPER. A body is projected vertically upwards at time t = 0 and is seen at a heiht at time t and t seconds durin its fliht. The maximum heiht attained is [ =
More informationPhys207: Lecture 04. Today s Agenda 3-D Kinematics Independence of x and y components Baseball projectile Shoot the monkey Uniform circular motion
Phys7: Lecture 4 Reminders All Discussion and Lab sections start meetin this week Homework is posted on course website Solutions to preious hwks will be posted Thursday mornins Today s Aenda 3-D Kinematics
More informationMotion in Two Dimensions Sections Covered in the Text: Chapters 6 & 7, except 7.5 & 7.6
Motion in Two Dimensions Sections Covered in the Tet: Chapters 6 & 7, ecept 7.5 & 7.6 It is time to etend the definitions we developed in Note 03 to describe motion in 2D space. In doin so we shall find
More informationREVIEW: Going from ONE to TWO Dimensions with Kinematics. Review of one dimension, constant acceleration kinematics. v x (t) = v x0 + a x t
Lecture 5: Projectile motion, uniform circular motion 1 REVIEW: Goin from ONE to TWO Dimensions with Kinematics In Lecture 2, we studied the motion of a particle in just one dimension. The concepts of
More informationBallistics Car P3-3527
WWW.ARBORSCI.COM Ballistics Car P3-3527 BACKGROUND: The Ballistic Car demonstrates that the horizontal motion of an object is unaffected by forces which act solely in the vertical direction. It consists
More informationPROJECTILE MOTION. ( ) g y 0. Equations ( ) General time of flight (TOF) General range. Angle for maximum range ("optimum angle")
PROJECTILE MOTION Equations General time of fliht (TOF) T sin θ y 0 sin( θ) General rane R cos( θ) T R cos θ sin( θ) sin( θ) y 0 Anle for maximum rane ("optimum anle") θ opt atan y 0 atan v f atan v f
More informationPrince Sultan University Physics Department First Semester 2012 /2013. PHY 105 First Major Exam Allowed Time: 60 min
Prince Sultan University Physics Department First Semester 01 /01 PHY 105 First Major Exam Allowed Time: 60 min Student Name: 1. Write your name in the specified space NOW.. Any paper without name will
More informationLinear Motion. Miroslav Mihaylov. February 13, 2014
Linear Motion Miroslav Mihaylov February 13, 2014 1 Vector components Vector A has manitude A and direction θ with respect to the horizontal. On Fiure 1 we chose the eastbound as a positive x direction
More informationGround Rules. PC1221 Fundamentals of Physics I. Position and Displacement. Average Velocity. Lectures 7 and 8 Motion in Two Dimensions
PC11 Fundamentals of Physics I Lectures 7 and 8 Motion in Two Dimensions Dr Tay Sen Chuan 1 Ground Rules Switch off your handphone and paer Switch off your laptop computer and keep it No talkin while lecture
More informationPhysics 111. Lecture 7 (Walker: 4.2-5) 2D Motion Examples Projectile Motion
Physics 111 Lecture 7 (Walker: 4.-5) D Motion Eamples Projectile Motion Sept. 16, 9 -D Motion -- Constant Acceleration r r r r = v t at t v t a t y y yt y v t at r r r v = v at v = v a t v = v a t y y
More informationDo not turn over until you are told to do so by the Invigilator.
UNIVERSITY OF EAST ANGLIA School of Mathematics Main Series UG Examination 2016 17 ENGINEERING MATHEMATICS AND MECHANICS ENG-4004Y Time allowed: 2 Hours Attempt QUESTIONS 1 and 2, and ONE other question.
More informationAAPT UNITED STATES PHYSICS TEAM AIP 2009
2009 F = ma Exam 1 AAPT UNITED STATES PHYSICS TEAM AIP 2009 2009 F = ma Contest 25 QUESTIONS - 75 MINUTES INSTRUCTIONS DO NOT OPEN THIS TEST UNTI YOU ARE TOD TO BEGIN Use = 10 N/k throuhout this contest.
More informationProjectile Motion. Chin- Sung Lin STEM GARAGE SCIENCE PHYSICS
Projectile Motion Chin- Sung Lin Introduction to Projectile Motion q What is Projectile Motion? q Trajectory of a Projectile q Calculation of Projectile Motion Introduction to Projectile Motion q What
More informationPHYS 100: Lecture 4 PROJECTILE MOTION. y = (v 0 /v T ) x (g/2v T2 )x 2. Velocity of Train v T. Physics 100 Lecture 4, Slide y(m)
PHYS : Lecture 4 PROJECTILE MOTION.4. Velocity of Train T y(m).8.6.4. 5 5 x(m) y ( / T ) x (/ T )x Physics Lecture 4, Slide Music Who is the Artist? A) Miles Dais B) Wynton Marsalis C) Chris Botti D) Nina
More information2.5 Velocity and Acceleration
82 CHAPTER 2. VECTOR FUNCTIONS 2.5 Velocity and Acceleration In this section, we study the motion of an object alon a space curve. In other words, as the object moves with time, its trajectory follows
More informationPHYS 1114, Lecture 9, February 6 Contents:
PHYS 4, Lecture 9, February 6 Contents: Continued with projectile motion: The kicko problem in football was treated analytically, obtainin formulas for maimum heiht and rane in terms of initial speed and
More informationVector Valued Functions
SUGGESTED REFERENCE MATERIAL: Vector Valued Functions As you work throuh the problems listed below, you should reference Chapters. &. of the recommended textbook (or the equivalent chapter in your alternative
More informationMathematics Extension 1 Time allowed: 2 hours (plus 5 minutes reading time)
Name: Teacher: Class: FORT STREET HIGH SCHOOL 0 HIGHER SCHOOL CERTIFICATE COURSE ASSESSMENT TASK : TRIAL HSC Mathematics Extension Time allowed: hours (plus 5 minutes readin time) Syllabus Assessment Area
More informationThis Week. Next Week
This Week Tutorial and Test 1, in the lab (chapters 1 and 2) Next Week Experiment 1: Measurement of Lenth and Mass WileyPLUS Assinment 1 now available Due Monday, October 5 at 11:00 pm Chapters 2 & 3 28
More informationGeodesics as gravity
Geodesics as ravity February 8, 05 It is not obvious that curvature can account for ravity. The orbitin path of a planet, for example, does not immediately seem to be the shortest path between points.
More informationMASSACHUSETTS INSTITUTE OF TECHNOLOGY Department of Physics. Physics 8.01x Fall Term 2001 EXAM 1 SOLUTIONS
MASSACHUSETTS INSTITUTE OF TECHNOLOGY Department of Physics Physics 8.01x Fall Term 2001 EXAM 1 SOLUTIONS Problem 1: We define a vertical coordinate system with positive upwards. The only forces actin
More informationPhysics 11 Fall 2012 Practice Problems 2 - Solutions
Physics 11 Fall 01 Practice Problems - s 1. True or false (inore any effects due to air resistance): (a) When a projectile is fired horizontally, it takes the same amount of time to reach the round as
More informationTo explore and investigate projectile motion and how it can be applied to various problems.
NAME: ΔY = 0 Projectile Motion Computer Lab Purpose: To explore and investigate projectile motion and how it can be applied to various problems. Procedure: 1. First, go to the following web site http://galileoandeinstein.physics.virginia.edu/more_stuff/applets/projectile
More information7.2 Maximization of the Range of a Rocket
138 CHAPTER 7. SOME APPLICATIONS The counterintuitive answer that a supersonic aircraft must dive first in order to climb to a iven altitude in minimum time was first discovered by Walter Denham and Art
More informationDynamics 4600:203 Homework 03 Due: February 08, 2008 Name:
Dynamics 4600:03 Homework 03 Due: ebruary 08, 008 Name: Please denote your answers clearly, i.e., bo in, star, etc., and write neatly. There are no points for small, messy, unreadable work... please use
More informationTransformations of Quadratic Functions
.1 Transormations o Quadratic Functions Essential Question How do the constants a, h, and k aect the raph o the quadratic unction () = a( h) + k? The parent unction o the quadratic amil is. A transormation
More informationExperiment 3 The Simple Pendulum
PHY191 Fall003 Experiment 3: The Simple Pendulum 10/7/004 Pae 1 Suested Readin for this lab Experiment 3 The Simple Pendulum Read Taylor chapter 5. (You can skip section 5.6.IV if you aren't comfortable
More informationProjectile motion. Objectives. Assessment. Assessment. Equations. Physics terms 5/20/14. Identify examples of projectile motion.
Projectile motion Objectives Identify examples of projectile motion. Solve projectile motion problems. problems Graph the motion of a projectile. 1. Which of the events described below cannot be an example
More informationWhen a is positive, the parabola opens up and has a minimum When a is negative, the parabola opens down and has a maximum
KEY CONCEPTS For a quadratic relation of the form y = ax 2 + c, the maximum or minimum value occurs at c, which is the y-intercept. When a is positive, the parabola opens up and has a minimum When a is
More informationUNIVERSITY OF SASKATCHEWAN Department of Physics and Engineering Physics
UNIVRSITY OF SASKATCHWAN Department of Physics and nineerin Physics Physics 115.3 MIDTRM TST October 3, 009 Time: 90 minutes NAM: (Last) Please Print (Given) STUDNT NO.: LCTUR SCTION (please check): 01
More informationSTUDY PACKAGE. Subject : PHYSICS Topic : KINEMATICS. Available Online :
fo/u fopkjr Hkh# tu] uha vkjehks dke] foifr ns[k NksM+s rqjar e/;e eu dj ';kea iq#"k fla ladyi dj] lrs foifr vusd] ^cuk^ u NksM+s /;s; dks] j?kqcj jk[ks VsdAA jfpr% ekuo /kez iz.ksrk ln~xq# Jh j.knksm+nklth
More informationEVERYDAY EXAMPLES OF ENGINEERING CONCEPTS
EVERYDAY EXAMPLES OF ENGINEERING CONCEPTS D3: Work & Ener Copriht 03 This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivs 3.0 Unported License. To view a cop of this license,
More informationProjectile Motion Exercises
Projectile Motion 11.7 Exercises 1 A ball is thrown horizontally from a cliff with a speed of 10ms-I, at the same time as an identical ball is dropped from the cliff. Neglecting the effect of air resistance
More informationStoichiometry of the reaction of sodium carbonate with hydrochloric acid
Stoichiometry of the reaction of sodium carbonate with hydrochloric acid Purpose: To calculate the theoretical (expected) yield of product in a reaction. To weih the actual (experimental) mass of product
More informationExperiment 1: Simple Pendulum
COMSATS Institute of Information Technoloy, Islamabad Campus PHY-108 : Physics Lab 1 (Mechanics of Particles) Experiment 1: Simple Pendulum A simple pendulum consists of a small object (known as the bob)
More informationProjectile Motion (Photogates)
Projectile Motion (Photogates) Name Section Theory Projectile motion is the combination of different motions in the x and y direction. In the x direction, which is taken as parallel to the surface of the
More informationPhysics 18 Spring 2011 Homework 2 - Solutions Wednesday January 26, 2011
Physics 18 Sprin 011 Homework - s Wednesday January 6, 011 Make sure your name is on your homework, and please box your final answer. Because we will be ivin partial credit, be sure to attempt all the
More informationAssignment 6. Name MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
Assinment 6 Name MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Round your answer, if appropriate. 1) A man 6 ft tall walks at a rate of 3 ft/sec
More information3.2 Projectile Motion
Motion in 2-D: Last class we were analyzing the distance in two-dimensional motion and revisited the concept of vectors, and unit-vector notation. We had our receiver run up the field then slant Northwest.
More informationLABORATORY II DESCRIPTION OF MOTION IN TWO DIMENSIONS
LABORATORY II DESCRIPTION OF MOTION IN TWO DIMENSIONS This laboratory allows you to continue the study of accelerated motion in more realistic situations. The cars you used in Laboratory I moved in only
More informationjfpr% ekuo /kez iz.ksrk ln~xq# Jh j.knksm+nklth egkjkt
Phone : 0 903 903 7779, 98930 58881 Kinematics Pae: 1 fo/u fopkjr Hkh# tu] uha kjehks dke] foifr ns[k NksM+s rqjar e/;e eu dj ';kea iq#"k fla ladyi dj] lrs foifr usd] ^cuk^ u NksM+s /;s; dks] j?kqcj jk[ks
More informationPhysics 121k Exam 3 7 Dec 2012
Answer each question and show your work. A correct answer with no supportin reasonin may receive no credit. Unless directed otherwise, please use =10.0 m/s 2. Name: 1. (15 points) An 5.0 k block, initially
More informationMidterm Feb. 17, 2009 Physics 110B Secret No.=
Midterm Feb. 17, 29 Physics 11B Secret No.= PROBLEM (1) (4 points) The radient operator = x i ê i transforms like a vector. Use ɛ ijk to prove that if B( r) = A( r), then B( r) =. B i = x i x i = x j =
More informationPhysics 201 Homework 1
Physics 201 Homework 1 Jan 9, 2013 1. (a) What is the magnitude of the average acceleration of a skier who, starting (a) 1.6 m/s 2 ; (b) 20 meters from rest, reaches a speed of 8.0 m/s when going down
More informationANALYZE In all three cases (a) (c), the reading on the scale is. w = mg = (11.0 kg) (9.8 m/s 2 ) = 108 N.
Chapter 5 1. We are only concerned with horizontal forces in this problem (ravity plays no direct role). We take East as the +x direction and North as +y. This calculation is efficiently implemented on
More informationMotion in Two Dimension (Projectile Motion)
Phsics Motion in Two Dimension (Projectile Motion) www.testprepkart.com Table of Content. Introdction.. Projectile. 3. Assmptions of projectile motion. 4. Principle of phsical independence of motions.
More informationPlanar Motion with Constant Acceleration
Planar Motion with Constant Acceleration 1. If the acceleration vector of an object is perpendicular to its velocity vector, which of the following must be true? (a) The speed is changing. (b) The direction
More information6 Mole Concept. g mol. g mol. g mol ) + 1( g : mol ratios are the units of molar mass. It does not matter which unit is on the
What is a e? 6 Mole Concept The nature of chemistry is to chane one ecule into one or more new ecules in order to create new substances such as paints, fertilizers, food additives, medicines, etc. When
More informationUNIVERSITY OF SASKATCHEWAN Department of Physics and Engineering Physics
UNIVRSITY OF SASKATCHWAN Department of Physics and nineerin Physics Physics 115.3 MIDTRM TST Alternative Sittin October 009 Time: 90 minutes NAM: (Last) Please Print (Given) STUDNT NO.: LCTUR SCTION (please
More information3.4 Projectile Motion
3.4 Projectile Motion Projectile Motion A projectile is anything launched, shot or thrown---i.e. not self-propelled. Examples: a golf ball as it flies through the air, a kicked soccer ball, a thrown football,
More informationUniversity of Alabama Department of Physics and Astronomy. PH 125 / LeClair Fall Exam III Solution
University of Alabama Department of Physics and Astronomy PH 5 / LeClair Fall 07 Exam III Solution. A child throws a ball with an initial speed of 8.00 m/s at an anle of 40.0 above the horizontal. The
More informationMechanics Cycle 3 Chapter 12++ Chapter 12++ Revisit Circular Motion
Chapter 12++ Revisit Circular Motion Revisit: Anular variables Second laws for radial and tanential acceleration Circular motion CM 2 nd aw with F net To-Do: Vertical circular motion in ravity Complete
More informationLab 5: Projectile Motion
Concepts to explore Scalars vs. vectors Projectiles Parabolic trajectory As you learned in Lab 4, a quantity that conveys information about magnitude only is called a scalar. However, when a quantity,
More information1. Adjust your marble launcher to zero degrees. Place your marble launcher on a table or other flat surface or on the ground.
Conceptual Physics Mrs. Mills Your Name: Group members: Lab: Marble Launcher Purpose: In this lab you will be using the marble launchers in order to examine the path of a projectile. You will be using
More informationPhysics 20 Homework 1 SIMS 2016
Physics 20 Homework 1 SIMS 2016 Due: Wednesday, Auust 17 th Problem 1 The idea of this problem is to et some practice in approachin a situation where you miht not initially know how to proceed, and need
More informationIn this activity, we explore the application of differential equations to the real world as applied to projectile motion.
Applications of Calculus: Projectile Motion ID: XXXX Name Class In this activity, we explore the application of differential equations to the real world as applied to projectile motion. Open the file CalcActXX_Projectile_Motion_EN.tns
More informationChapter 8 ~ Quadratic Functions and Equations In this chapter you will study... You can use these skills...
Chapter 8 ~ Quadratic Functions and Equations In this chapter you will study... identifying and graphing quadratic functions transforming quadratic equations solving quadratic equations using factoring
More informationProjectile Motion. x = v ox t (1)
Projectile Motion Theory Projectile motion is the combination of different motions in the x and y directions. In the x direction, which is taken as parallel to the surface of the earth, the projectile
More informationExam 1 Practice SOLUTIONS Physics 111Q.B
Exam 1 Practice SOLUTIONS Physics 111Q.B Instructions This is a collection of practice problems for the first exam. The first exam will consist of 7-10 multiple choice questions followed by 1-3 problems
More information2.3. PBL Equations for Mean Flow and Their Applications
.3. PBL Equations for Mean Flow and Their Applications Read Holton Section 5.3!.3.1. The PBL Momentum Equations We have derived the Reynolds averaed equations in the previous section, and they describe
More informationLab 4: Projectile Motion
59 Name Date Partners OVEVIEW Lab 4: Projectile Motion We learn in our study of kinematics that two-dimensional motion is a straightforward extension of one-dimensional motion. Projectile motion under
More informationStudent Instruction Sheet: Unit 3, Lesson 3. Solving Quadratic Relations
Student Instruction Sheet: Unit 3, Lesson 3 Solving Quadratic Relations Suggested Time: 75 minutes What s important in this lesson: In this lesson, you will learn how to solve a variety of quadratic relations.
More informationLABORATORY II DESCRIPTION OF MOTION IN TWO DIMENSIONS
LABORATORY II DESCRIPTION OF MOTION IN TWO DIMENSIONS In this laboratory you continue the study of accelerated motion in more situations. The carts you used in Laboratory I moved in only one dimension.
More informationPROJECTILES. Launched at an Angle
PROJECTILES Launched at an Anle PROJECTILE MOTION AT AN ANGLE An bject launched int space withut mtie pwer f its wn is called a prjectile. If we nelect air resistance, the nly frce actin n a prjectile
More informationGround Rules. PC1221 Fundamentals of Physics I. Position and Displacement. Average Velocity. Lectures 7 and 8 Motion in Two Dimensions
PC11 Fndamentals of Physics I Lectres 7 and 8 Motion in Two Dimensions A/Prof Tay Sen Chan 1 Grond Rles Switch off yor handphone and paer Switch off yor laptop compter and keep it No talkin while lectre
More informationAltitude measurement for model rocketry
Altitude measurement for model rocketry David A. Cauhey Sibley School of Mechanical Aerospace Enineerin, Cornell University, Ithaca, New York 14853 I. INTRODUCTION In his book, Rocket Boys, 1 Homer Hickam
More informationExercise. Accelerated Math : Monday, May 6, 2013, 7:40 PM Mr. J. Ziarno Ziarno-1st James Ziarno
of 9 Accelerated Math : Monday, May 6, 0, 7:40 PM Mr. J. Ziarno Melourne Central Catholic Hih School Form Numer 90 (Rerint). Is f ( x ) = x + a one-to-one function?. Determine which of the followin is
More informationGRADE 11 EXAMINATION NOVEMBER EXAMINER: Mrs C Jacobsz. MODERATORs: Ms M Eastes, Mrs T Thorne and Mrs V Rixon
GRADE 11 EXAMINATION NOVEMBER 2015 DURBAN GIRLS' COLLEGE MATHEMATICS PAPER 1 TIME: 3 HOURS 150 MARKS EXAMINER: Mrs C Jacobsz MODERATORs: Ms M Eastes, Mrs T Thorne and Mrs V Rion PLEASE READ THE FOLLOWING
More informationHomework # 2. SOLUTION - We start writing Newton s second law for x and y components: F x = 0, (1) F y = mg (2) x (t) = 0 v x (t) = v 0x (3)
Physics 411 Homework # Due:..18 Mechanics I 1. A projectile is fired from the oriin of a coordinate system, in the x-y plane (x is the horizontal displacement; y, the vertical with initial velocity v =
More informationA Mathematical Model for the Fire-extinguishing Rocket Flight in a Turbulent Atmosphere
A Mathematical Model for the Fire-extinuishin Rocket Fliht in a Turbulent Atmosphere CRISTINA MIHAILESCU Electromecanica Ploiesti SA Soseaua Ploiesti-Tiroviste, Km 8 ROMANIA crismihailescu@yahoo.com http://www.elmec.ro
More informationCHAPTER 4 GENERAL MOTION OF A PARTICLE IN THREE DIMENSIONS
CHAPTER 4 GENERAL MOTION OF A PARTICLE IN THREE DIMENSIONS --------------------------------------------------------------------------------------------------------- Note to instructors there is a tpo in
More informationLab 5: Projectile Motion
Lab 5 Projectile Motion 47 Name Date Partners Lab 5: Projectile Motion OVERVIEW We learn in our study of kinematics that two-dimensional motion is a straightforward application of onedimensional motion.
More informationExam 2A Solution. 1. A baseball is thrown vertically upward and feels no air resistance. As it is rising
Exam 2A Solution 1. A baseball is thrown vertically upward and feels no air resistance. As it is risin Solution: Possible answers: A) both its momentum and its mechanical enery are conserved - incorrect.
More informationDesign of Chevron Gusset Plates
017 SEAOC CONENTION PROCEEDINGS Desin of Chevron Gusset Plates Rafael Sali, Director of Seismic Desin Walter P Moore San Francisco, California Leih Arber, Senior Enineer American Institute of Steel Construction
More informationLab 10: Ballistic Pendulum
Lab Section (circle): Day: Monday Tuesday Time: 8:00 9:30 1:10 2:40 Lab 10: Ballistic Pendulum Name: Partners: Pre-Lab You are required to finish this section before coming to the lab it will be checked
More informationProjectiles 6D. 1 At maximum height, h, the vertical component of velocity, vy = 0, a = g, s h, v 0 R( ) sin. v u 2as sin 2. U h. as required.
Projectiles 6D 1 At maimum heiht, h, the ertical component of elocit, = 0 R( ): u u sin, a =, s h, 0 u as 0 sin h sin h sin h Resolin the initial elocit horizontall and erticall R( ) u 1cos R u 1sin a
More informationNick Egbert MA 158 Lesson 6. Recall that we define +,,, / on functions by performing these operations on the outputs.
Nick Ebert MA 158 Lesson 6 Function arithmetic Recall that we define +,,, / on functions by performin these operations on the outputs. So we have (f + )(x) f(x) + (x) (f )(x) f(x) (x) (f)(x) f(x)(x) (
More informationPIRATE SHIP EXAMPLE REPORT WRITE UP
PIRATE SHIP EXAMPE REPORT WRITE UP Title Aim period Pirate Ship investiation To find the relationship between the lenth of a pendulum and its Independent variable the lenth of the pendulum. I will use
More informationInstructor Quick Check: Question Block 12
Instructor Quick Check: Question Block 2 How to Administer the Quick Check: The Quick Check consists of two parts: an Instructor portion which includes solutions and a Student portion with problems for
More informationProperties of Graphs of Quadratic Functions
Properties of Graphs of Quadratic Functions y = ax 2 + bx + c 1) For a quadratic function given in standard form a tells us: c is the: 2) Given the equation, state the y-intercept and circle the direction
More informationLesson 1: What is a Parabola?
Lesson 1: What is a Parabola? Parabola Vocabulary Write the defintion of the given word. Label #3-6 on the graph. 1. Parabola: Name Class Date 2. Trajectory: 3. Zeros: 4. Axis of Symmetry: 5. Vertex: Online
More informationMs. Peralta s IM3 HW 5.4. HW 5.4 Solving Quadratic Equations. Solve the following exercises. Use factoring and/or the quadratic formula.
HW 5.4 HW 5.4 Solving Quadratic Equations Name: Solve the following exercises. Use factoring and/or the quadratic formula. 1. 2. 3. 4. HW 5.4 5. 6. 4x 2 20x + 25 = 36 7. 8. HW 5.4 9. 10. 11. 75x 2 30x
More informationBell Ringer: What is constant acceleration? What is projectile motion?
Bell Ringer: What is constant acceleration? What is projectile motion? Can we analyze the motion of an object on the y-axis independently of the object s motion on the x-axis? NOTES 3.2: 2D Motion: Projectile
More informationPurpose: Materials: WARNING! Section: Partner 2: Partner 1:
Partner 1: Partner 2: Section: PLEASE NOTE: You will need this particular lab report later in the semester again for the homework of the Rolling Motion Experiment. When you get back this graded report,
More informationWord Problems: Solving a System of Equations (Quadratic/ Linear)
Word Problems: Solving a System of Equations (Quadratic/ Linear) l 1. Consider the line passing through points A (0,7) and B (3,1) and the parabola with vertex V (1,1) passing through the point C ( 1,9).
More information