Projectile Launched Horizontally
|
|
|
- Maude Foster
- 5 years ago
- Views:
Transcription
1 Projectile Launched Horizontally by Nada Saab-Ismail, PhD, MAT, MEd, IB nhsaab.weebly.com P3.3c Explain the recoil of a projectile launcher in terms of forces and masses. P3.4e Solve problems involving force, mass, and acceleration in two-dimensional projectile motion restricted to an initial horizontal velocity with no initial vertical velocity (e.g., a ball rolling off a table).
2 Projectile Launched Horizontally Projectile launched at zero angle ( = 0) is a free fall with an initial horizontal velocity (vo). This is an example of projectile launched horizontally with an angle = 0 comparing to the horizontal.
3 Characteristics of Projectile Motion Projectile motion is the motion of objects moving in two dimensions horizontal (vx) and vertical (vy). In Projectile motion: the horizontal motion and the vertical motion are independent of each other. Neither motion affects the other. the initial vertical velocity is zero (voy = 0), but increases regularly because of the acceleration due to gravity (g). So, vy increases along the path. the initial horizontal velocity (vox) stays the same along the path (vox = vx = constant).
4 Example 1: Below is an example of projectile launched horizontally. a) Notice that the initial horizontal velocity (vox) stays the same along the path (vox = vx = constant = 20 m/s).
5 b) Notice that at launch there is no initial vertical velocity (voy = 0). Later; the vertical velocity vy increases along the path from -9.8 m/s to m/s to m/ s to m/s to m/s when it reaches the ground.
6 Example 2: A Falling Care Package: The figure below shows airplane moving horizontally with a constant velocity of +115 m/s at an altitude of 1050m. The direction to the right and upward have been chosen as the positive directions. The plane releases a care package that falls to the ground along a curved trajectory.
7 Notice that the care package remains directly under the plane all the time, as the dashed line shows for the following reasons: a) Both the plane and care package travel at a constant velocity vox = vx = 115 m/s. b) the initial vertical velocity is zero (voy = 0), but increases regularly because of the acceleration due to gravity (g). So, vy increases along the path. c) the horizontal motion and the vertical motion are independent of each other. Neither motion affects the other.
8 Vertical motion of projectile and free fall The vertical motion of projectile launched horizontally is identical to that of a dropped object. Verification: A strobe-light photo of two balls released simultaneously from a mechanism that allows one ball to drop freely (red) while the other is projected horizontally ( yellow). Notice that at equal times, both balls fall the same vertical distance. Both hit the ground at the same time.
9 Example 3: The figure below shows two packages A and B. Package B is given an initial velocity component Vx = 115 m/s in the horizontal direction. The package follows a path as shown in the figure. Package A, on the other hand, is dropped from a stationary balloon and falls straight down toward the ground (Vx = 0 m/s). Both packages A and B hit the ground at the same time.
10 Kinematic Equations for Projectile Motion The basic kinematics equations are used with the components of motion. X axis: Variable along the x axis: x, vx, vox, ax, t Horizontal Component of Motion: 1. ax = 0 (acceleration along the x axis) 2. vx = vox = constant Kinematic equations: Projectile launched horizontally at an angle X components: Velocity component along the x axis (vox) vox = vo = constant Range R or Landing site x X= R = vox t Notice that the horizontal velocity component (vox) does not change because it is not a function of time.
11 y axis: Variable along the y axis: y, vy, voy, ay, t Horizontal Component of Motion: 1. ay = g ( m/s 2 ) = acceleration due to gravity directed down toward the center of the Earth. 2. voy is not constant Y components; Kinematic equations: Projectile launched horizontally at an angle Velocity components along the y axis at different times (vy). Maximum height launched y or H vy = g t H = y = 1 g (t) 2 2 t; time
12 Time and total velocity Kinematic equations: Projectile launched horizontally at an angle Time to reach the ground or hang time t 2 = 2 y / g The total velocity at a specific instant (v) 2 = (vo) 2 + (vy) 2 The angle the projectile reaches the ground The angle ( ) the projectile reaches the ground tangent = tan. Kinematic equations: Projectile launched horizontally at an angle tan = vy / vx = tan -1 vy / vx) Cos = vx / v = Cos -1 vx / v)
13 Example 4: A Falling Care Package: The figure below shows airplane moving horizontally with a constant velocity of +115 m/s at an altitude of 1050m. The direction to the right and upward have been chosen as the positive directions. The plane releases a care package that falls to the ground along a curved trajectory.
14 Ignoring air resistance, determine: a- the time required for the care package to hit the ground (t) b- the landing site of the care package, or range (R) c- the vertical velocity of the care package when it hits the ground (Vy) d- the final velocity of the care package (V). We know that acceleration along the y axis is ay = g = m/s 2 Data Table vo ay y t x vy v 115 m/s g = m/s m? R???
15 Equations for Projectile Launched Horizontally ( = 0) vox : Velocity component along the x axis, always the same. vox = vo = +115 m/s t: time to reach the ground. t 2 = 2 y/g = 2 (-1050)/ m/s 2 = s 2 t = 14.6 s X: Landing site x = vox t = (115 m/s) (14.6 s) = 1679 m vy :velocity components along the y axis at different times. vy = g t = ( -9.8 m/s 2 )(14.6 s) = -143 m/s negative because it is directed down. Total velocity the instant before reaching the ground, or at any instant (v) 2 = (vo) 2 + (vy) 2 = (115 m/s) 2 + (-143 m/s) 2 = (m/s) 2 v = 184 m/s
16 We can calculate the angle when the care package hits the ground > = tan -1 vy / vx) = tan -1 (143/ 115) = 51.2 o or = cos -1 vx / v) = cos -1 (115/ 184) = 51.3 o
17 Example 5:
18 Example 6: A Rescue Plane A rescue plane flies at constant horizontal velocity of 55.0 m/s and constant height of 500 m toward a point directly over a victim, where a rescue capsule is to land. The plane drops a rescue capsule. While falling the capsule remains under the plane. Data Table vo ay y t x vy v 55 m/s g = m/s m? R???
19 References: 1) Humanic. (2013). In Thomas Humanic Brochure Page. Physics 1200 Lecture Slides: Dr. Thomas Humanic, Professor of Physics, Ohio State University, and Current. 2) Cutnell, J. D. & Johnson, K. W. (1998). Cutnell & Johnson Physics, Fourth Edition. New York: John Wiley & Sons, Inc. The edition was dedicated to the memory of Stella Kupferberg, Director of the Photo Department: We miss you, Stella, and shall always remember that a well-chosen photograph should speak for itself, without the need for a lengthy explanation
20 3) Martindale, D. G. & Heath, R. W. & Konrad, W. W. & Macnaughton, R. R. & Carle, M. A. (1992). Heath Physics. Lexington: D.C. Heath and Company 4) Zitzewitz, P. W. (1999). Glencoe Physics Principles and Problems. New York: McGraw-Hill Companies, Inc. 5) Schnick, W.J. (n.d.). Calculus-based physics, A Free Physics Textbook. Retrieved from 6) Nada H. Saab (Saab-Ismail), ( ) Westwood Cyber High School, Physics. 7) Nada H. Saab (Saab-Ismail), ( ) Wayne RESA, Bilingual Department.
Since a projectile moves in 2-dimensions, it therefore has 2 components just like a resultant vector: Horizontal Vertical
Since a projectile moves in 2-dimensions, it therefore has 2 components just like a resultant vector: Horizontal Vertical With no gravity the projectile would follow the straight-line path (dashed line).
Zero Launch Angle. since θ=0, then v oy =0 and v ox = v o. The time required to reach the water. independent of v o!!
Zero Launch Angle y h since θ=0, then v oy =0 and v ox = v o and based on our coordinate system we have x o =0, y o =h x The time required to reach the water independent of v o!! 1 2 Combining Eliminating
20/06/ Projectile Motion. 3-7 Projectile Motion. 3-7 Projectile Motion. 3-7 Projectile Motion
3-7 A projectile is an object moving in two dimensions under the influence of Earth's gravity; its path is a parabola. 3-7 It can be understood by analyzing the horizontal and vertical motions separately.
Projectile Trajectory Scenarios
Projectile Trajectory Scenarios Student Worksheet Name Class Note: Sections of this document are numbered to correspond to the pages in the TI-Nspire.tns document ProjectileTrajectory.tns. 1.1 Trajectories
Projectile Motion SECTION 3. Two-Dimensional Motion. Objectives. Use of components avoids vector multiplication.
Projectile Motion Key Term projectile motion Two-Dimensional Motion Previously, we showed how quantities such as displacement and velocity were vectors that could be resolved into components. In this section,
Two-Dimensional Motion
Two-Dimensional Motion Objects don't always move in a straight line. When an object moves in two dimensions, we must look at vector components. The most common kind of two dimensional motion you will encounter
OCR Maths M2. Topic Questions from Papers. Projectiles
OCR Maths M2 Topic Questions from Papers Projectiles PhysicsAndMathsTutor.com 21 Aparticleisprojectedhorizontallywithaspeedof6ms 1 from a point 10 m above horizontal ground. The particle moves freely under
Preview. Two-Dimensional Motion and Vectors Section 1. Section 1 Introduction to Vectors. Section 2 Vector Operations. Section 3 Projectile Motion
Two-Dimensional Motion and Vectors Section 1 Preview Section 1 Introduction to Vectors Section 2 Vector Operations Section 3 Projectile Motion Section 4 Relative Motion Two-Dimensional Motion and Vectors
Math Learning Center Boise State 2010, Quadratic Modeling STEM 10
Quadratic Modeling STEM 10 Today we are going to put together an understanding of the two physics equations we have been using. Distance: Height : Recall the variables: o acceleration o gravitation force
Projectile Motion. A.1. Finding the flight time from the vertical motion. The five variables for the vertical motion are:
Projectile Motion A. Finding the muzzle speed v0 The speed of the projectile as it leaves the gun can be found by firing it horizontally from a table, and measuring the horizontal range R0. On the diagram,
Vector Decomposition
Projectile Motion AP Physics 1 Vector Decomposition 1 Coordinate Systems A coordinate system is an artificially imposed grid that you place on a problem. You are free to choose: Where to place the origin,
2.3 Projectile Motion
Figure 1 An Olympic ski jumper uses his own body as a projectile. projectile an object that moves along a two-dimensional curved trajectory in response to gravity projectile motion the motion of a projectile
SPH3U1 Lesson 12 Kinematics
SPH3U1 Lesson 12 Kinematics PROJECTILE MOTION LEARNING GOALS Students will: Describe the motion of an object thrown at arbitrary angles through the air. Describe the horizontal and vertical motions of
Stomp Rocket Lab Physics
Stomp Rocket Lab Physics Stomp Rockets are plastic projectiles that are launched when a bladder of air is hit or stomped with a foot. Typically the launch angle can be changed, but should be left at 90
(ii) Calculate the maximum height reached by the ball. (iii) Calculate the times at which the ball is at half its maximum height.
1 Inthis question take g =10. A golf ball is hit from ground level over horizontal ground. The initial velocity of the ball is 40 m s 1 at an angle α to the horizontal, where sin α = 0.6 and cos α = 0.8.
Name Period. (b) Now measure the distances from each student to the starting point. Write those 3 distances here. (diagonal part) R measured =
Lesson 5: Vectors and Projectile Motion Name Period 5.1 Introduction: Vectors vs. Scalars (a) Read page 69 of the supplemental Conceptual Physics text. Name at least 3 vector quantities and at least 3
Projectile Motion. Honors Physics
Projectile Motion Honors Physics What is projectile? Projectile -Any object which projected by some means and continues to moe due to its own inertia (mass). Projectiles moe in TWO dimensions Since a projectile
Date Course Name Instructor Name Student(s) Name WHERE WILL IT LAND?
Date Course Name Instructor Name Student(s) Name WHERE WILL IT LAND? You have watched a ball roll off a table and strike the floor. What determines where it will land? Could you predict where it will land?
Edexcel Mechanics 2 Kinematics of a particle. Section 1: Projectiles
Edecel Mechanics Kinematics of a particle Section 1: Projectiles Notes and Eamples These notes contain subsections on Investigating projectiles Modelling assumptions General strateg for projectile questions
PROJECTILE MOTION PURPOSE
PURPOSE The purpose of this experiment is to study the motion of an object in two dimensions. The motion of the projectile is analyzed using Newton's laws of motion. During the motion of the projectile,
Purpose of the experiment
Projectile Motion PES 116 Advanced Physics Lab I Purpose of the experiment Measure the velocity of a ball using two photogates and Logger Pro. Apply the concepts of two-dimensional kinematics to predict
Graphical Analysis of Kinematics
Physics Topics Graphical Analysis of Kinematics If necessary, review the following topics and relevant textbook sections from Serway / Jewett Physics for Scientists and Engineers, 9th Ed. Velocity and
Chapter 3: Vectors & 2D Motion. Brent Royuk Phys-111 Concordia University
Chapter 3: Vectors & 2D Motion Brent Royuk Phys-111 Concordia University Vectors What is a vector? Examples? Notation:! a or! a or a 2 Vector Addition Graphical Methods Triangle, parallelogram, polygon
Graphical Analysis of Kinematics
Physics Topics Graphical Analysis of Kinematics If necessary, review the following topics and relevant textbook sections from Serway / Jewett Physics for Scientists and Engineers, 9th Ed. Velocity and
Lab 4 Projectile Motion
b Lab 4 Projectile Motion What You Need To Know: x = x v = v v o ox = v + v ox ox + at 1 t + at + a x FIGURE 1 Linear Motion Equations The Physics So far in lab you ve dealt with an object moving horizontally
Name Class Date. Activity P37: Time of Flight versus Initial Speed (Photogate)
Name Class Date Activity P37: Time of Flight versus Initial Speed (Photogate) Concept DataStudio ScienceWorkshop (Mac) ScienceWorkshop (Win) Projectile motion P37 Time of Flight.DS P08 Time of Flight P08_TOF.SWS
Two-Dimensional Projectile Motion
Two-Dimensional Projectile Motion I. Introduction. This experiment involves the study of motion using a CCD video camera in which a sequence of video frames (a movie ) is recorded onto computer disk and
PROJECTILE. 5) Define the terms Velocity as related to projectile motion: 6) Define the terms angle of projection as related to projectile motion:
1) Define Trajectory a) The path traced by particle in air b) The particle c) Vertical Distance d) Horizontal Distance PROJECTILE 2) Define Projectile a) The path traced by particle in air b) The particle
Review for Quarter 3 Cumulative Test
Review for Quarter 3 Cumulative Test I. Solving quadratic equations (LT 4.2, 4.3, 4.4) Key Facts To factor a polynomial, first factor out any common factors, then use the box method to factor the quadratic.
2. The diagram shows part of the graph of y = a (x h) 2 + k. The graph has its vertex at P, and passes through the point A with coordinates (1, 0).
Quadratics Vertex Form 1. Part of the graph of the function y = d (x m) + p is given in the diagram below. The x-intercepts are (1, 0) and (5, 0). The vertex is V(m, ). (a) Write down the value of (i)
Unit 2: Functions and Graphs
AMHS Precalculus - Unit 16 Unit : Functions and Graphs Functions A function is a rule that assigns each element in the domain to exactly one element in the range. The domain is the set of all possible
Projectile Motion. Remember that the projectile travels vertically (up and down y) in the same time that it is traveling above the horizontal (x)
Projectile Motion Consider motion in and y separately Ignore air resistance elocity in -direction is constant Write down positions in and y as a function of time Remember that the projectile traels ertically
Projectile Motion. Photogate 2 Photogate 1 Ramp and Marble. C-clamp. Figure 1
Projectile Motion Purpose Apply concepts from two-dimensional kinematics to predict the impact point of a ball in projectile motion, and compare the result with direct measurement. Introduction and Theory
LAB 03: The Equations of Uniform Motion
LAB 03: The Equations of Uniform Motion This experiment uses a ramp and a low-friction cart. If you give the cart a gentle push up the ramp, the cart will roll upward, slow and stop, and then roll back
Goals: - to be able to recognize the position-time, velocity-time and acceleration-time graphs of each of these main types of motion:
Unit: One-Dimensional Kinematics Level: 1 Prerequisites: None Points to: Goals: - to be able to recognize the position-time, velocity-time and acceleration-time graphs of each of these main types of motion:
Contents 10. Graphs of Trigonometric Functions
Contents 10. Graphs of Trigonometric Functions 2 10.2 Sine and Cosine Curves: Horizontal and Vertical Displacement...... 2 Example 10.15............................... 2 10.3 Composite Sine and Cosine
Contents 10. Graphs of Trigonometric Functions
Contents 10. Graphs of Trigonometric Functions 2 10.2 Sine and Cosine Curves: Horizontal and Vertical Displacement...... 2 Example 10.15............................... 2 10.3 Composite Sine and Cosine
4.5 Conservative Forces
4 CONSERVATION LAWS 4.5 Conservative Forces Name: 4.5 Conservative Forces In the last activity, you looked at the case of a block sliding down a curved plane, and determined the work done by gravity as
Precalculus 2 Section 10.6 Parametric Equations
Precalculus 2 Section 10.6 Parametric Equations Parametric Equations Write parametric equations. Graph parametric equations. Determine an equivalent rectangular equation for parametric equations. Determine
Lesson 3.1 Vertices and Intercepts. Important Features of Parabolas
Lesson 3.1 Vertices and Intercepts Name: _ Learning Objective: Students will be able to identify the vertex and intercepts of a parabola from its equation. CCSS.MATH.CONTENT.HSF.IF.C.7.A Graph linear and
Lecture 5. If, as shown in figure, we form a right triangle With P1 and P2 as vertices, then length of the horizontal
Distance; Circles; Equations of the form Lecture 5 y = ax + bx + c In this lecture we shall derive a formula for the distance between two points in a coordinate plane, and we shall use that formula to
Displacement-time and Velocity-time Graphs
PhysicsFactsheet April Number Displacement- and Velocity- Graphs This Factsheet explains how motion can be described using graphs, in particular how - graphs and - graphs can be used. Displacement- graphs
You are going to need to access the video that was taken of your device - it can be accessed here:
Part 2: Projectile Launcher Analysis Report Submit Assignment Due Dec 17, 2015 by 10:30am Points 100 Submitting a file upload Available after Dec 17, 2015 at 6am Step 2 - Now We Look At The Real World
We ve defined vectors as quantities that have a magnitude and a direction Displacement, velocity, and acceleration Represent by an arrow whose length
We ve defined vectors as quantities that have a magnitude and a direction Displacement, velocity, and acceleration Represent by an arrow whose length represents magnitude and head represents direction
ROSE-HULMAN INSTITUTE OF TECHNOLOGY
Introduction to Working Model Welcome to Working Model! What is Working Model? It's an advanced 2-dimensional motion simulation package with sophisticated editing capabilities. It allows you to build and
Practice Exams. Exam logistics. Projectile Motion Problem-Solving. ax = 0 m/s2 ay = -9.8 m/s2. You won t do well if you wait then cram.
1 v projectile is in free fall! ax = 0 m/s2 ay = -9.8 m/s2 Projectile Motion Problem-Solving Last year s exam equation sheet. 2 What are you getting stuck on in problem-solving? Topics: Chapters 1 3 including:
Physics 2210 Fall smartphysics 02 Kinematics in 2- and 3-d 08/31/2015
Physics 2210 Fall 2015 smartphysics 02 Kinematics in 2- and 3-d 08/31/2015 Supplemental Instruction Schedule Tuesdays 8:30-9:20 am..jwb 308 Wednesdays 3:00-3:50 pm JFB B-1 Thursdays 11:30am - 12:20 pm...lcb
Motion Graphs. Plotting position against time can tell you a lot about motion. Let's look at the axes:
Motion Graphs 1 Name Motion Graphs Describing the motion of an object is occasionally hard to do with words. Sometimes graphs help make motion easier to picture, and therefore understand. Remember: Motion
Recitation 1-6 Projectile Motion
Preliminaries Recitation 1-6 Projectile Motion The Recorder is the youngest person at your table. The Recorder Should write down everyone s name on the worksheet and put your Table No. on the worksheet.
Kinematics Review. Physics 2012
Kinematics Review Physics 2012 Question 1 Mom and Junior are driving north in a car. They pass Spike who is standing on the side of the road. Which of these statements are correct? 1. Spike sees mom and
Types of Functions Here are six common types of functions and examples of each. Linear Quadratic Absolute Value Square Root Exponential Reciprocal
Topic 2.0 Review Concepts What are non linear equations? Student Notes Unit 2 Non linear Equations Types of Functions Here are six common types of functions and examples of each. Linear Quadratic Absolute
Find the component form and magnitude of the vector where P = (-3,4), Q = (-5, 2), R = (-1, 3) and S = (4, 7)
PRE-CALCULUS: by Finney,Demana,Watts and Kennedy Chapter 6: Applications of Trigonometry 6.1: Vectors in the Plane What you'll Learn About Two Dimensional Vectors/Vector Operations/Unit Vectors Direction
Free Fall. Objective. Materials. Part 1: Determining Gravitational Acceleration, g
Free Fall Objective Students will work in groups to investigate free fall acceleration on the Earth. Students will measure the fundamental physical constant, g, and evaluate the dependence of free fall
How do you roll? Fig. 1 - Capstone screen showing graph areas and menus
How do you roll? Purpose: Observe and compare the motion of a cart rolling down hill versus a cart rolling up hill. Develop a mathematical model of the position versus time and velocity versus time for
Applied Parabolas: Catapult (one test grade)
Name: I. Overview: PreCalculus Applied Parabola Project Applied Parabolas: Catapult (one test grade) You will use catapults to launch candy into the air. Using a stopwatch, you will time how long the projectile
2D Kinematics Projectiles Relative motion
2D Kinematics Projectiles Relative motion Lana heridan De Anza College Oct 4, 2017 Last time 2 dimensional motion projectile motion height of a projectile Overview range of a projectile trajectory equation
Practice problems from old exams for math 233
Practice problems from old exams for math 233 William H. Meeks III October 26, 2012 Disclaimer: Your instructor covers far more materials that we can possibly fit into a four/five questions exams. These
sin30 = sin60 = cos30 = cos60 = tan30 = tan60 =
Precalculus Notes Trig-Day 1 x Right Triangle 5 How do we find the hypotenuse? 1 sinθ = cosθ = tanθ = Reciprocals: Hint: Every function pair has a co in it. sinθ = cscθ = sinθ = cscθ = cosθ = secθ = cosθ
ME 105 Homework 4 A Movie Stunt Simulation with Graphical User Interface
ME 105 Homework 4 A Movie Stunt Simulation with Graphical User Interface In the 1994 action-adventure film Speed, a Los Angeles bus with a bomb that was set to explode if the speed of the buss fell below
Physics 101, Lab 1: LINEAR KINEMATICS PREDICTION SHEET
Physics 101, Lab 1: LINEAR KINEMATICS PREDICTION SHEET After reading through the Introduction, Purpose and Principles sections of the lab manual (and skimming through the procedures), answer the following
EEN118 LAB FOUR. h = v t ½ g t 2
EEN118 LAB FOUR In this lab you will be performing a simulation of a physical system, shooting a projectile from a cannon and working out where it will land. Although this is not a very complicated physical
Quadratic Functions CHAPTER. 1.1 Lots and Projectiles Introduction to Quadratic Functions p. 31
CHAPTER Quadratic Functions Arches are used to support the weight of walls and ceilings in buildings. Arches were first used in architecture by the Mesopotamians over 4000 years ago. Later, the Romans
AA Simulation: Firing Range
America's Army walkthrough AA Simulation: Firing Range Firing Range This simulation serves as an introduction to uniform motion and the relationship between distance, rate, and time. Gravity is removed
Falling Balls. Names: Date: About this Laboratory
Falling Balls Names: Date: About this Laboratory In this laboratory,1 we will explore quadratic functions and how they relate to the motion of an object that is dropped from a specified height above ground
Slide 2 / 222. Algebra II. Quadratic Functions
Slide 1 / 222 Slide 2 / 222 Algebra II Quadratic Functions 2014-10-14 www.njctl.org Slide 3 / 222 Table of Contents Key Terms Explain Characteristics of Quadratic Functions Combining Transformations (review)
7-5 Parametric Equations
3. Sketch the curve given by each pair of parametric equations over the given interval. Make a table of values for 6 t 6. t x y 6 19 28 5 16.5 17 4 14 8 3 11.5 1 2 9 4 1 6.5 7 0 4 8 1 1.5 7 2 1 4 3 3.5
Visual Physics Camera Parallax Lab 1
In this experiment you will be learning how to locate the camera properly in order to identify and minimize the sources of error that are introduced by parallax and perspective. These sources of error
Lecture 4. If P1(x1,y1) and P2(x2,y2) are points on a non-vertical line, then the slope m of the line is defined by
Lines Lecture 4 In this section we shall discuss ways to measure the "steepness" or "slope" of a line in the plane. The ideas we develop here will be important when we discuss equations and graphs of straight
EEN118 LAB FOUR. h = v t ½ g t 2
EEN118 LAB FOUR In this lab you will be performing a simulation of a physical system, shooting a projectile from a cannon and working out where it will land. Although this is not a very complicated physical
Goals: Course Unit: Describing Moving Objects Different Ways of Representing Functions Vector-valued Functions, or Parametric Curves
Block #1: Vector-Valued Functions Goals: Course Unit: Describing Moving Objects Different Ways of Representing Functions Vector-valued Functions, or Parametric Curves 1 The Calculus of Moving Objects Problem.
Position vs Time Graphs *
OpenStax-CNX module: m54110 1 Position vs Time Graphs * OpenStax HS Physics This work is produced by OpenStax-CNX and licensed under the Creative Commons Attribution License 4.0 1 : By the end of this
Quadratic Functions, Part 1
Quadratic Functions, Part 1 A2.F.BF.A.1 Write a function that describes a relationship between two quantities. A2.F.BF.A.1a Determine an explicit expression, a recursive process, or steps for calculation
(40-455) Student Launcher
611-1415 (40-455) Student Launcher Congratulations on your purchase of the Science First student launcher. You will find Science First products in almost every school in the world. We have been making
Detailed instructions for video analysis using Logger Pro.
Detailed instructions for video analysis using Logger Pro. 1. Begin by locating or creating a video of a projectile (or any moving object). Save it to your computer. Most video file types are accepted,
EEN118 LAB FOUR. h = v t ½ g t 2
EEN118 LAB FOUR In this lab you will be performing a simulation of a physical system, shooting a projectile from a cannon and working out where it will land. Although this is not a very complicated physical
SPH3U1 Lesson 09 Kinematics
VECTORS IN TWO-DIMENSIONS LEARNING GOALS Students will Draw vector scale diagrams to visualize and analyze the nature of motion in a plane. Analyze motion by using scale diagrams to add vectors. Solve
Math 4: Advanced Algebra Ms. Sheppard-Brick A Quiz Review LT ,
4A Quiz Review LT 3.4 3.10, 4.1 4.3 Key Facts Know how to use the formulas for projectile motion. The formulas will be given to you on the quiz, but you ll need to know what the variables stand for Horizontal:
Learning Objectives. Math Prerequisites. Technology Prerequisites. Materials. Math Objectives. Technology Objectives
Learning Objectives Parametric Functions Lesson 2: Dude, Where s My Football? Level: Algebra 2 Time required: 60 minutes Many students expect a falling object graph to look just like the path of the falling
Ball Toss. Data Pro program. 2. Make a sketch of your prediction for the velocity vs. time graph. Describe in words what this graph means.
Ball Toss Experiment 34 When a juggler tosses a ball straight upward, the ball slows down until it reaches the top of its path. The ball then speeds up on its way back down. A graph of its velocity vs.
EEN118 LAB FOUR. h = v t - ½ g t 2
EEN118 LAB FOUR In this lab you will be performing a simulation of a physical system, shooting a projectile from a cannon and working out where it will land. Although this is not a very complicated physical
Armstrong State University Engineering Studies MATLAB Marina Algorithm Development I Primer
Armstrong State University Engineering Studies MATLAB Marina Algorithm Development I Primer Prerequisites The Algorithm Development I Primer assumes knowledge of the MATLAB IDE, MATLAB help, arithmetic
On-line Virtual Kinematics Laboratory Visualizing Interactively Projectile Motion
On-line Virtual Kinematics Laboratory Visualizing Interactively Projectile Motion Author: A. Milazzo, A. Bonanno Dipartimento di Fisica Università della Calabria. Unità I.N.F.M. di Cosenza. Introduction
Self-Correcting Projectile Launcher. Josh Schuster Yena Park Diana Mirabello Ryan Kindle
Self-Correcting Projectile Launcher Josh Schuster Yena Park Diana Mirabello Ryan Kindle Motivation & Applications Successfully reject disturbances without use of complex sensors Demonstrate viability of
Chapter 4: Kinematics of Rigid Bodies
Chapter 4: Kinematics of Rigid Bodies Advanced Dynamics Lecturer: Hossein Nejat Fall 2016 A rigid body is defined to be a collection of particles whose distance of separation is invariant. In this circumstance,
SPH3U1 Lesson 05 Kinematics
VECTORS IN TWO-DIMENSIONS LEARNING GOALS Students will Draw vector scale diagrams to visualize and analyze the nature of motion in a plane. Analyze motion by using scale diagrams to add vectors. Solve
Honors Pre-Calculus. 6.1: Vector Word Problems
Honors Pre-Calculus 6.1: Vector Word Problems 1. A sled on an inclined plane weighs 00 lb, and the plane makes an angle of 0 degrees with the horizontal. What force, perpendicular to the plane, is exerted
BLM Answers. BLM 4-1 Prerequisite Skills. BLM 4-3 Section 4.1 Modelling With Quadratic Relations. 10. a)
BLM Answers (page 1) BLM 4-1 Prerequisite Skills 1. a) 11.1 2.7 9.0 d) 20.2 2. a) 1.7 10.7 6.5 d) 25.1 3. a) 9.5 20.7 96 d) 31.85 4. a) 3x 6x 2 + 6x + 5 10x 2 2x + 6 d) 12x 2 + 10x 6 5. a) 5 0 12 d) 2
Algebra II. Chapter 13 Notes Sections 13.1 & 13.2
Algebra II Chapter 13 Notes Sections 13.1 & 13.2 Name Algebra II 13.1 Right Triangle Trigonometry Day One Today I am using SOHCAHTOA and special right triangle to solve trig problems. I am successful
Functions and Transformations
Using Parametric Representations to Make Connections Richard Parr T 3 Regional, Stephenville, Texas November 7, 009 Rice University School Mathematics Project rparr@rice.edu If you look up parametric equations
Motion Graphs. Plotting distance against time can tell you a lot about motion. Let's look at the axes:
Motion Graphs 1 _ Motion Graphs Describing the motion of an object is occasionally hard to do with words. Sometimes graphs help make motion easier to picture, and therefore understand. Remember: Motion
Lab #4: 2-Dimensional Kinematics. Projectile Motion
Lab #4: -Dimensional Kinematics Projectile Motion A medieval trebuchet b Kolderer, c1507 http://members.iinet.net.au/~rmine/ht/ht0.html#5 Introduction: In medieval das, people had a ver practical knowledge
Unit 6 Quadratic Functions
Unit 6 Quadratic Functions 12.1 & 12.2 Introduction to Quadratic Functions What is A Quadratic Function? How do I tell if a Function is Quadratic? From a Graph The shape of a quadratic function is called
Toy animal ball poppers provide a great way to use projectile motion in the classroom. We used
Using Toy Animal Ball Poppers to Explore Projectile Motion in Algebra and Calculus Classes Marsha Nicol Guntharp, Palm Beach Atlantic University Fred Browning, Palm Beach Atlantic University Gloria Royle,
Centroid Principles. Object s center of gravity or center of mass. Graphically labeled as
Centroids Centroid Principles Object s center of gravity or center of mass. Graphically labeled as Centroid Principles Point of applied force caused by acceleration due to gravity. Object is in state of
Study Guide and Review - Chapter 10
State whether each sentence is true or false. If false, replace the underlined word, phrase, expression, or number to make a true sentence. 1. A triangle with sides having measures of 3, 4, and 6 is a
Study Guide and Review - Chapter 10
State whether each sentence is true or false. If false, replace the underlined word, phrase, expression, or number to make a true sentence. 1. A triangle with sides having measures of 3, 4, and 6 is a
Factor Quadratic Expressions
Factor Quadratic Expressions BLM 6... BLM 6 Factor Quadratic Expressions Get Ready BLM 6... Graph Quadratic Relations of the Form y = a(x h) + k. Sketch each parabola. Label the vertex, the axis of symmetry,
Sphero Lightning Lab Cheat Sheet
Actions Tool Description Variables Ranges Roll Combines heading, speed and time variables to make the robot roll. Duration Speed Heading (0 to 999999 seconds) (degrees 0-359) Set Speed Sets the speed of
3.1 Investigating Quadratic Functions in Vertex Form
Math 2200 Date: 3.1 Investigating Quadratic Functions in Vertex Form Degree of a Function - refers to the highest exponent on the variable in an expression or equation. In Math 1201, you learned about
Parametric Representation throughout Pre-Calculus Richard Parr Rice University School Mathematics Project
Parametric Representation throughout Pre-Calculus Richard Parr Rice University School Mathematics Project rparr@rice.edu If you look up parametric equations in the index of most Pre-Calculus books, you