...A projectile is a body in free fall that is subject only to the forces of gravity (9.81ms‾²) and air resistance (Webster). It was Galileo who first accurately described projectile motion. He showed that it could be understood by analyzing the horizontal and vertical components separately. No one had done this prior to Galileo. People use to think that when something is shot in the air it goes in the air and some how hit something and explode, before Galileo which followed largely Aristotelian lines but incorporating a later theory of "impetus," which maintained that an object shot from a cannon, for example, followed a straight line until it "lost its impetus," at which point it fell abruptly to the ground. Later, simply by more careful observation, it was realized that projectiles actually follow a curved path. Yet no one knew what that path was, until Galileo. There was yet another brilliant insight that led Galileo to his most astounding conclusion about projectile motion. First of all, he reasoned that a projectile is not only influenced by one motion, but by two. The motion that acts vertically is the force of gravity, and this pulls an object towards the earth at 9.8 meters per second. But while gravity is pulling the object down, the projectile is also moving forward, horizontally at the same time. And this horizontal motion is uniform and constant according to Galileo's principle of inertia. He was indeed able to show that a projectile is controlled by two independent...
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...(a) Marks Let f ( x ) = x 3 + 5 x 2 + 17 x − 10. The equation f ( x ) = 0 has only one real root. 4 (i) Show that the root lies between 0 and 2. (ii) Use one application of the ‘halving the interval’ method to find a smaller interval containing the root. (iii) Which end of the smaller interval found in part (ii) is closer to the root? Briefly justify your answer. Consider the equation 4 x 3 + 6 x 2 − x − 30 = 0. One of the roots of this equation is equal to the sum of the other two roots. Find the values of the three roots. 1996 (a) ( x − 2) is a factor of the polynomial P( x ) = 2 x 3 + x + a . Find the value of a. Marks The function f ( x ) = x 3 − ln( x + 1) has one root between 0·5 and 1. (i) (b) Show that the root lies between 0·8 and 0·9. (ii) Hence use the halving-the-interval method to find the value of the root, correct to one decimal place. 1997 (b) A particle is moving in simple harmonic motion. Its displacement x at time t is given by 4 x = 3 sin(2t + 5) . (i) Find the period of the motion. (ii) Find the maximum acceleration of the particle. (iii) (c) Find the speed of the particle when x = 2 . The polynomial P( x ) = x 3 + bx 2 + cx + d has roots 0, 3, and –3. (i) Find b, c, and d. (ii) Without using calculus, sketch the graph of y = P( x ) . (iii) Hence, or otherwise, solve the inequality x2 − 9 all over x > 0. 1998 Let α, β and γ be the roots of the polynomial 2x3 − 14x − 1 = 0. Find αβγ . A...
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...Name ____Anjad itayem______________ Projectile Motion Go to http://phet.colorado.edu/simulations/sims.php?sim=Projectile_Motion and click on Run Now. Pre Lab Reflections: What are the • What forces are at play on a body under fall ? gravity and air resistance • Make a prediction of which angle results in maximum range. My prediction is that angel of 70 degrees will be the mazimum range Activity: - Open the sim, projectile motion. - Familiarize yourself with the variables shown there. - Ensure the air resistance check box remains unchecked. - Using the mouse set the angle of projection(i) to 5 deg. Alternatively enter the value in directly. - Set the initial speed to a value U=15m/s . - Click on Fire to start the projectile and record the corresponding value of the range R. - Repeat with values i= 10,15,20,25,30,35,40,45,50,60,70,75,80,85. - Draw a graph of Range (R) against Angle of projection (i) You may want your lay out to appear like in the table. U=……… |Angle (i) |Range(m) | |5 |9.7 | |10 |12.2 | |15 |14.9 | |20 |17.5 | |30 |21.8 | |35 |23.2 ...
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...Air Resistance Formula We have seen the planes moving in sky what decreases its speed? This is what Air resistance is! [pic] Air resistance is the resistance against the air, which decreases the speed of the moving object. Its formula is given as [pic] Where c is air constant, v is the object's velocity. Air Resistance Formula is used to find the air resistance, air constant and velocity of body if some of these quantities are known. This formula has wide applications in aeronautics. Air resistance Problems Back to Top Below are given some problems based on air resistance which may be helpful for you. Solved Examples Question 1: A plane moving with velocity of 50 ms-1 has a force constant of 0.05. Calculate its air resistance. Solution: Given: Velocity of air v = 50 ms-1, Force constant c = 0.05 The force constant is given by F = cv2 = 0.05 × 2500 = 125 N. Question 2: An object is traveling at 20 ms-1 experiences a force of 50 N. Calculate the force constant. Solution: Given: Velocity of air v = 20 ms-1, Force F = 50 N, The force constant is given by c = F/v² = 50/20² = 0.125 http://formulas.tutorvista.com/physics/air-resistance-formula.html#air-resistance-problems http://physics.tutorvista.com/motion/projectile-motion.html • PhysicsMotionProjectile Motion Top ...
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...3/12/14 A Defense of Hedonism Many objections have been made against the theory of axiological hedonism. I will not attempt to respond to all of them, but instead focus on one of the stronger arguments, which deals with life trajectories. I will begin by briefly presenting the theory of axiological hedonism and then present the objection regarding life trajectories to the best of my ability. Finally for the majority of my essay, I will argue for why this objection is unsound and does not prove that hedonism is false. Axiological hedonism is the philosophical theory that is based on the idea that the only thing in this world that is intrinsically good for its own sake is happiness. This is different from the theory of psychological hedonism, which says that the only thing humans are physically able to desire for its own sake is happiness. First developed by Epicurus and later revised by John Stuart Mill along with many others, the theory of axiological hedonism uses a distinction between what philosophers call instrumental goods and things that are intrinsically valuable to illustrate its claim. Instrumental goods are any things in the world that are valuable because of the good things they bring about. Things that are intrinsically valuable on the other hand, are things that are inherently good for their own sake. Axiological hedonism claims that happiness is the only thing that is intrinsically valuable. The argument for axiological hedonisms is roughly as follows: ...
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...INTERNATIONAL ANTALYA UNIVERSITY COLLAGE OF ENGINEERING PHYSICS 101 LABORATORY REPORT NUMBER OF LAB SESSION: 2 EXPERIMENTS: 1- The Relationship between Time of Flight and Initial Velocity 2- Projectile Motion 3- Projectile Range versus Angle AUTHOR OF THIS REPORTS: FULL NAME: RANA AKMAN STUDENT NO: 140201038 LAB SECTION: OTHER EXPERIMENTER: FULL NAME: EDA HAZAL RAŞİT STUDENT NO: 140203009 EXPERIMENT PERFORMED ON: 30/09/2015 REPORT SUBMITTED ON: 07/10/2015 EXPERIMENT 1: The Relationship between Time of Flight and Initial Velocity Equipments: 1. Projectile launcher 2. Time-of-Flight Accessory 3. Xplorer GLX (as timing device) 4. Yellow Nylon Ball (2.5 cm diameter, 10 g) 5. Photogate 6. Photogate bracket 7. Carbon paper 8. White paper 9. Measuring tape 10. Duct tape Purpose: Purpose of this experiment is to Procedure: I have equipment to measured the fall time and I have different ball. This lesson was my first LAB so I didn’t know anything about equipments...
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...howstuffworks.com) A projectile is any object which once projected or dropped continues in motion by its own inertia ( the property of matter by which it retains its velocity so long as it is not acted upon by an external force) and is influenced only by the downward force of gravity. By definition, a projectile has only one force acting upon it - the force of gravity. There are a variety of examples of projectiles. An object dropped from rest is a projectile. An object which is thrown vertically upward is also a projectile. And an object which is thrown upward at an angle to the horizontal is also a projectile. Projectile motion is simply the motion of an object in a plane (two dimensions) under the influence of gravity. The trajectory describes an arc. The equations of motion describe the components of such motion and are useful to analyze projectile motion. In textbook problems, the initial velocity of an object is typically given, and the subsequent motion is described with equations of motion. The method used in this lab will be to determine the initial velocity of a projectile from range-fall measurements. If a projectile is launched horizontally with an initial velocity of magnitude vox = vo from a height of y, then the projectile will travel a horizontal distance x (the range of the...
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...Title: To investigate the trajectory of a small ball as it rolls off a surface which is inclined to the horizontal. Objectives: To investigate the trajectory of a two dimensional motion. Apparatus and materials: Ramp, wooden block, pendulum bob, plumb line, steel ball, wooden board, carbon paper, meter ruler, plasticine. Setup: 1. A ramp was set up at the edge of a bench. 2. A plum-line is suspended from the edge of the bench. 3. A wooden board is mounted horizontally using two clamps so that the board is situated about the bottom of the ramp. 4. A sheet of blank paper is placed on top of the board. 5. A piece of carbon paper is placed on the top of the blank paper. The ink-side of the carbon paper is facing down. 6. When a ball was released from the top of the ramp, the ball travelled through a trajectory. Theory: Let: g= 9.80ms-2 u= speed of the ball as it leaves the ramp k= constant y= vertical distance (between the bottom of the ramp and the top of the board) x= horizontal distance (between the plum-line and mark on the paper) The equation which relates x and y is yx=g1+k2x2u2+k Procedure : 1. The ball was positioned at the top of the ramp. The ball was released so that it rolls down the...
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...opponent off balance by limiting their own offensive opportunities. There are two main types of serves in volleyball: The underhand serve and the overhand serve. Both types of serves can be broken down into three main components: * Serving posture: The athlete’s body position—correct weight distribution and ideal arm and foot placement—before the actual serve. * The toss: The lifting or throwing of the ball into the air before contact is made. Discussions about the toss usually focus on correct ball positioning, the ideal toss height for each type of serve, and preferred toss techniques. * Contact point: The position of the server’s hand upon the moment of contact. The contact point is significant because it determines the trajectory of the ball. This guide will discuss both basic types of serves in terms of the concepts outlined above because each stage is critical to the successful execution of the serve. The Underhand Serve The underhand serve is a great option for beginning players because it is the easiest of the three types of serves to master. Since every rally begins with a serve, the primary goal of any inexperienced server should be to just put the ball into play. Posture Practicing good underhand serving posture prepares you to be a consistent underhand server and can also prepare you for overhand serving. Here are some serving posture tips to keep in mind: * Feet should be slightly staggered with the foot opposite your hitting arm out in front...
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...diagrams best represents the subsequent path of the ball? (1) 2. An archer shoots an arrow at an angle to the horizontal. Air resistance is negligible. Which of the following graphs best represents the variation with time of the horizontal component of the arrow’s velocity from the time it is launched to the time just before it hits the ground? (1) 3. The diagram below shows the path of a projectile in the absence of air resistance. Which one of the following diagrams best represents the path of the projectile under the same initial conditions when the air resistance is taken into account? (The path in absence of air resistance is shown for comparison as a dotted line.) (1) 4. This question is about the trajectory of a golf ball. A golfer hits a golf ball at point A on a golf course. The ball lands at point D as shown on the diagram. Points A and D are on the same horizontal level. The initial horizontal component of the velocity of the ball is 20 m s–1 and the initial vertical component is 30 m s–1. The time of flight of the golf ball between point A and point D is 6.0 s. Air resistance is negligible and the acceleration of free fall g = 10 m s–2. Calculate (a) the maximum height reached by the golf ball. ................................................................................................................................... .......................................................................................................
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...Week 2 Thought Paper CJE4610 8/31/14 A case starts the moment the call is received. In many cases there is evidence or clues on the call itself. One of the things you can get from the call is a description of the incident, suspect information, and other various clues and information. Then when you get on scene your real investigation will begin. You may or may not have real life suspects or victims on scene. Once you get on scene you have to start processing information and the scene itself. You never know what clues you will get when you show up on scene. There are different types of evidence to collect when you process a scene. There is trace evidence, which includes hairs, fibers, glass and soil. The second is impression evidence, which includes fingerprints left on objects, and also palms, tires and cloth. The next kind of evidence is biological to include blood, teeth and skeletal remains. The fourth kind of evidence is firearms and weapons including the guns and ammunition. The last is probably the one that most people forget or disregard, are documents to include contracts, currency, passports, and other documents. In the case that was presented on page 126 there was a lot of evidence to be processed. The call originated as a disturbance from neighbors. The officers arrived and discovered a very disrupted house. From the pictures, there were obvious signs of a struggle with in the residence. So the description stated that when the officer arrived no one...
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...Name: Sharon Mohammed Candidate Number: School: Iere High School Class: Form 5s (Science) Project Title: Projectile Motion Additional Mathematics SBA: Teacher: Ms. Lia Chunilal Date: TABLE OF CONTENTS Project Title……………………………………………………………………………pg3 Aim of Project………………………………………………………………………..pg4 Problem Statement……………………………………………………………………pg5 Information about Volleyball…………………………………………………………pg9 Apparatus and Materials………………………………………………………………pg6 Method for Experiment……………………………………………………………….pg7 Solution to Problem…………………………………………………………………..pg8 Verification of Solution……………………………………………………………….pg18 Discussion……………………………………………………………………………..pg19 Conclusion…………………………………………………………………………….pg21 Bibliography...................................................................................................................pg22 PROJECT TITLE: To determine the ideal angle at which Penelope, a national volleyball player, needs to serve the ball in order to obtain the distance that it needs to go over the net but stay in the court y applying the theory of projectile motion. AIM: To determine the ideal angle and distance needed for a volleyball ball to be served over the net within the dimension of the court using projectile motion. PROBLEM STATEMENT: Penelope is a national volleyball player and she wants to know the angle at which she needs to serve the volleyball in order to get the ball over the net but also in the court every time she serves...
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...Tutorial 3: Projectile motion and Laws of motion. 1. Two crickets, Chirpy and Milada, jump from the top of a vertical cliff. Chirpy just drops from a vertical cliff with a height of 350 m, while Milada jumps horizontally with an initial speed of 8.0 m/s . How far from the base of the cliff will Milada hit the ground? [67.6 m] 2. A ball is given an initial velocity of 30.0 m/s at an angle of 60.0o with respect to the horizontal. What are the horizontal and vertical displacements after 5.00 s? [75.0 m, 7.40 m] 3. A soccer player kicks the ball toward a goal that is 16.8 m in front of him. The ball leaves his foot at a speed of 16.0 m/s and an angle of 28.0° above the ground. Find the speed of the ball when the goalie catches it in front of the net. [14.7 m/s] 4. The best leaper in the animal kingdom is the puma, which can jump to a height of 3.7 m when leaving the ground at an angle of 45°. With what speed must the animal leave the ground to reach that height? [12 m/s] 5. A fireman d = 50.0 m away from a burning building directs a stream of water from a ground-level fire hose at an angle of i = 30.0° above the horizontal as shown in figure. If the speed of the stream as it leaves the hose is vi = 40.0 m/s, at what height will the stream of water strike the building? [18.6 m] 6. A projectile is launched from ground level at an angle of 15.0° above the horizontal. It returns to ground level. To what value should the launch angle be adjusted...
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...increase population growth rate, r, while keeping carrying capacity steady. Decrease r? Sketch your results. By increasing the population growth rate, r, while keeping carrying capacity steady, leads the population to grow faster. By decreasing...
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...Sustainable Development and Planetary Boundaries BACKGROUND RESEARCH PAPER Johan Rockström and Jeffrey D. Sachs with Marcus C. Öhman and Guido Schmidt-Traub Submitted to the High Level Panel on the Post-2015 Development Agenda This paper reflects the views of the author and does not represent the views of the Panel. It is provided as background research for the HLP Report, one of many inputs to the process. May 2013 Draft for Discussion Sustainable Development and Planetary Boundaries Draft for Discussion Background paper for the High-Level Panel of Eminent Persons on the Post-2015 Development Agenda Prepared by the co-chairs of the Sustainable Development Solutions Network Thematic Group on Macroeconomics, Population Dynamics, and Planetary Boundaries: Johan Rockström Executive Director, Stockholm Resilience Centre Professor of Environmental Science, Stockholm University Jeffrey D. Sachs Director, The Earth Institute, Columbia University Director, The Sustainable Development Solutions Network Special Advisor to Secretary-General Ban Ki-Moon on the Millennium Development Goals with Marcus C. Öhman Associate Professor and Senior Researcher in Ecology and Environmental Science, Stockholm Resilience Centre Guido Schmidt-Traub Executive Director, The Sustainable Development Solutions Network 15 March 2013 1 Draft for Discussion The world faces a serious challenge, indeed one that is unique to our age. Developing countries rightly...
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