";s:4:"text";s:31671:"Note the construction of the height equation in the problem above. See Answer. In projectile motion problems, up is defined as the positive direction, so the y component has a magnitude of 49.0 m/s, in the down direction. The initial velocity (launch speed) was 19.6 m/s, and the coefficient on the linear term was "19.6". And in the equation "V = A*T" the 'V' referred to is the CHANGE in Velocity. Consider a projectile launched with an initial velocity of 50 m/s at an angle of 60 degrees above the horizontal. Consider the following example: An object is launched directly upward at 19.6 m/s from a 58.8-meter tall platform. g is gravitational acceleration. Newtonian mechanics : dynamics of a point mass (1001-1108) - Dynamics of a system of point masses (1109-1144) - Dynamics of rigid bodies (1145-1223) - Dynamics of deformable bodies (1224-1272) - Analytical mechanics : Lagrange's equations ... To illustrate the kinematic analysis, consider a projectile launched at point (Xo, Yo), with an initial velocity of Vo, having components (Vo)x and (Vo)y. 1. Therefore, to find the velocity of a particle in vertical displacement caused by the uniform acceleration of gravity is given by: V y = V y0 − gt. Welcome to Physics Notes: Physical Quantities and Motion. This book is the first in a series of books that when combined will cover all physics subject areas at pre-university standard. The horizontal velocity of a projectile is constant (a never changing in value), There is a vertical acceleration caused by gravity; its value is 9.8 m/s/s, down, The vertical velocity of a projectile changes by 9.8 m/s each second, The horizontal motion of a projectile is independent of its vertical motion. Projectile Motion Introduction In this lab you will study the motion of a freely-falling projectile, namely a small plastic sphere. Example In the given picture below, Alice throws the ball to the +X direction with an initial velocity 10m/s. Hence use this formula: u = sq rt (Sg/ sin2#) where, u = initial velocity 0. A. Lewis Ford, Texas A&M This manual includes worked-out solutions for about one-third of the problems. Volume 1 covers Chapters 1-17. Volume 2 covers Chapters 22-46. Answers to all odd-numbered problems are listed at the end of the book. Fully endorsed by OCR and revised to match the 2005 specification, this series has been carefully revised by experienced teachers and provides easy to use texts. The formula for time gives the time of flight of the projectile. Found insideThis book covers essential Microsoft EXCEL®'s computational skills while analyzing introductory physics projects. The vertical motion of a projectile is controlled by the force of gravity. Projectile motion is the motion of an object thrown or projected into the air, subject only to acceleration as a result of gravity. In the simplest kind of projectile motion problems, there is no initial velocity. Projectile Motion Formulas. (c) In projectile problems, horizontal component of initial velocity appears in the uniform motion along the horizontal direction as $\Delta x=v_{0x} t$, where $\Delta x$ is the horizontal distance. Found insideThe textbook covers the background theory of various effects discussed from first principles, as clearly as possible, to introduce students to the main ideas of quantum physics and to teach the basic mathematical methods and techniques used ... The horizontal motion of the projectile is the result of the tendency of any object in motion to remain in motion at constant velocity. Projectile Motion Formula A projectile is an object that is in flight after we throw it or project it. Thoughtful Physics for JEE Mains & Advanced – Kinematics: has been designed in keeping with the needs and expectations of students appearing for JEE Main and Advanced. The free-flight motion of a projectile is often studied in terms of its rectangular components. The equation used to calculate the vertical velocity of projectile motion: V y = v 0 - gt. This states that the final velocity that a projectile reaches equals its initial velocity value plus the product of the acceleration due to gravity and the time the object is in motion. This is always true for these up/down projectile motion … V x initial = V x final. Projectile motion is the motion of an object thrown (projected) into the air. But we were only giving the initial velocity of the ball, v 0, not the initial velocity in the x-direction, v x,0. The Initial Speed when the time of flight is given formula is defined as the velocity of the object before acceleration causes a change. "University Physics is a three-volume collection that meets the scope and sequence requirements for two- and three-semester calculus-based physics courses. The acceleration due to gravity is a universal constant. Derive an equation you could use to calculate total time of flight for an object launched . (b) We can find the final horizontal and vertical velocities … is initial velocity per second. The distance traveled in air is 35 m/ s x 2 seconds = 70 meters. This text is written for undergraduates who are studying orbital mechanics for the first time and have completed courses in physics, dynamics, and mathematics, including differential equations and applied linear algebra. Projectile motion problems and answers. Projectile Motion Formulas Questions: 1) A child kicks a soccer ball off of the top of a hill. Packed with science and a sense of humor, this book will improve readers' understanding of the world and how it works--and it may just improve their Angry Birds scores as well. The text explains key topics in algebra-based physics in clear, easy-to-understand language. "The best physics books are the ones kids will actually read." Advance Praise for APlusPhysics Regents Physics Essentials: "Very well written... simple, clear engaging and accessible. You hit a grand slam with this review book. Assuming that v 2 /g is constant, the greatest distance will be when sin (2θ) is at its maximum, which is when 2θ = … Its value is approximately 32 feet (9.8 meters) per second. Initial velocity of the projectile v 0 can be resolved into two components. To calculate projectile motion at an angle, first resolve the initial velocity into its horizontal and vertical components. You might have come across a formula like this: d = v 0 2 sin. This book is Learning List-approved for AP(R) Physics courses. The text and images in this book are grayscale. Following are the formula of projectile motion which is also known as trajectory formula: Where, V x is the velocity (along the x-axis) V xo is Initial velocity (along the x-axis) V y is the velocity (along the y-axis) V yo is initial velocity (along the y-axis) g is the acceleration due to gravity; t is the time taken; Equations related to the projectile motion is given as. As an object in projectile motion, the time of flight is only determined based on the initial height and the force of gravity. The path the object follows is called its trajectory. Find the time of flight and impact velocity of a projectile … The initial vertical velocity 'u v ' will be zero. The range of an object, given the initial launch angle and initial velocity is … V_x = Horizontal velocity. You should obtain an equation of the form where and are constants. These "Class 1 Problems" are when the projectile is launched horizontally. These are known as the horizontal and vertical components of the initial velocity. Find the maximum height it can reach, horizontal distance it covers and total time from the given information. Stack Exchange network consists of 177 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share … Notice that the location equation is pretty messy! The Formula for Maximum Height. Projectile Motion. Since this is projectile motion problem, however, there are different values for the object in the x and y direction. Calculate the range, time of flight, and maximum height of a projectile that is launched and impacts a flat, horizontal surface. (e.g. If the initial velocity is Vo, and the angle is a, then the vertical component of the velocity is Vy=Vo [sin (a)], and the horizontal component is Vx=Vo [cos (a)]. The formulas used in the resolution of projectile motion problems are the same as the constant velocity motion and the uniformly accelerated motion formulas, something that is important to know is that in most of the projectile motion problems we are going to have a general velocity, so we have to learn how to decompose the velocity. Learn horizontal range formula here. How do i find the initial velocity? Final velocity before the object hits the ground 2. 1 5 m / s. 15\, {\rm m/s} 15m/s at an angle 37° above the horizontal (neglect the air resistance). Initial Velocity (V 0) [m/s] Initial Horizontal Velocity (V 0x) Initial Vertical Velocity (V 0y) Final Velocity (V f) Final Horizontal Velocity (V fx) Final Vertical Velocity (V fy) Initial Height (y 0) [m] Final Height (y f) Maximum Height (h) Horizontal Distance (l) Flight Duration (t) [s] After that, the horizontal range is depending upon the initial velocity \(V_{0}\), the launch angle \(\theta\), and the acceleration occurring due to the gravity. Projectile motion, for our purposes, is the motion of an object that has been launched and then is subject to only the force of gravity and the force of air friction. The book uses different approaches to solve the differential equations of projectile motion — among them the Siacci method and the numerical methods. V y = … vy = uy + ayt v y = u y + a y t. v2 y = u2 y + 2ays v y 2 = u y 2 + 2 a y s. s represents the vertical displacement, ay represents the acceleration in the vertical axis (gravity), uy and vy are the initial vertical velocity and velocity after time t of the object during its projectile motion. Offers advice for using physics concepts to increase the realism of computer games, covering mechanics, real-world situations, and real-time simulations. Correct formula to find the range of a projectile (given angle (possibly negative), initial velocity, initial elevation, and g) 0. We can find the initial velocity with angle and distance if we know the time of motion. Also, the velocity of the particle changes from its initial value. Distance - Horizontal distance traveled is x = Vx x t (time) - Vertical distance from the ground is y = h + Vy x t – g (gravity) x t² / 2 Velocity - Horizontal velocity = Vx - Vertical velocity = Vy – g x t Acceleration - Horizontal acceleration = 0 - Vertical acceleration = -g (gravity acts on a projectile) 3. ... Photo-gates were then used to determine the initial velocity. It is important to read the question carefully and label your values accordingly. Hence the component of initial velocity (velocity of projection) parallel and perpendicular to the plane are equal to v 0 cos (θ – β) and v 0 sin (θ – β) respectively. For a given time t, we would have to find the local velocity V, and then plug that value into the location equation to get the location y. The two roots of this equation give you two possible angles. This means that there is an unbalanced force acting on the ball and so the ball will accelerate downwards. Analysis of projectile motion involves dealing with two motions independently. Equations of Motion. This motion is called vertical projectile motion. Formulas to calculate the velocity, distance and acceleration are as follows. Calculate the range, flight time and maximum height of a projectile launched and impact a flat, horizontal surface. Using the equation, d = vt for linear motion,. It is calculated through the vertical part and put into horizontal part to calculate the initial velocity. The arching of a thrown ball is caused by gravity, as well as its falling motion in general. Usually the object will be launched directly upward or dropped directly down. Projectile motion is the motion of an object who's path is affected by the force of gravity. The horizontal displacement of the projectile is called the range of the projectile, and depends on the initial velocity of the object. now after maximum height projectile will fall down and travel 25m distance vertical and initial velocity is zero hence use equation. Projectile Motion Lab - Determine the initial velocity of a ball launched horizontally Predict and verify. If the baseball has an initial horizontal velocity of 3 m/s, then at each point during its flight its horizontal velocity is also 3 m/s. The horizontal velocity of a projectile changes by 9.8 m/s each second. The two components are; v x0 = v 0 cos and v y0 = sin θ. So Maximum Height Formula is: Mathematically: H is maximum height. As per the time of flight formula, initial velocity, theta, and acceleration of gravity(g) are required to do calculations. To find initial velocity, start by multiplying the acceleration by the time. Found insideThis is the first comprehensive survey of the field of constraint databases, written by leading researchers. Constraint databases are a fairly new and active area of database research. This highly acclaimed text focuses on developing the abstract thinking essential for further mathematical study The authors give early, intensive attention to the skills necessary to make students comfortable with mathematical proofs. Trajectory Formula. This text blends traditional introductory physics topics with an emphasis on human applications and an expanded coverage of modern physics topics, such as the existence of atoms and the conversion of mass into energy. I'm trying to find the initial velocity of a tennis ball (magnitude and angle) given the initial height, max height and max range. The projectile motion is always in the form of a parabola which is represented as: y = ax + bx 2. Projectile motion is calculated by a way of neglecting air resistance in order to simplify the calculations. The above diagram represents the motion of an object under the influence of gravity. So, we can use trigonometry to calculate the initial x velocity: Equation 7: Plug that into Equation 6, and we have our final equation for x as a function of time: Equation 8: A projectile is an object that is given an initial velocity, and is acted on by gravity. The maximum height of the object in projectile motion depends on the initial velocity, the launch angle and the acceleration due to gravity. Use one-dimensional motion in perpendicular directions to analyze projectile motion. A projectile is an object that is given an initial velocity, and is acted on by gravity. Objects experiencing projectile motion have a constant velocity in the horizontal direction, and a constantly changing velocity in the vertical direction. Convenient access to information from every area of mathematics: Fourier transforms, Z transforms, linear and nonlinear programming, calculus of variations, random-process theory, special functions, combinatorial analysis, game theory, much ... Practice B: A motorcycle stunt person traveling 70 mi/hr jumps off a ramp at an angle of 35 degrees to the horizontal. Projectile Motion for Vertical Displacement Calculation I want to calculate Vertical Displacement at Time(Δy) Initial Vertical Velocity(Vy0) Acceleration of Gravity(g) Time(t) This means you will need to make two lists. An object is simply dropped so that the Earth’s magnetic field pulls it toward the ground at a rate of 9.81 m/s 2.This acceleration is all in a vertical direction (i.e. T = Time of flight. You need to find how long it takes for the object to go up, slow due to the acceleration of gravity, and then fall … Explanation: When you launch a projectile at an angle θ from the horizontal, the initial velocity of the projectile will have a vertical and a horizontal component. Choose upward as positive and downward as negative. Find the flight time and impact velocity of a projectile The goal is for readers to view the world through eyes that know physics. The new edition also features MasteringPhysics and an unparalleled suite of media and on-line resources to enhance the physics classroom. ... Projectile Motion Lab - Determine the initial velocity of a ball launched horizontally Predict and verify. use a value between 0 and 90 degrees) or the velocity. Initial velocity at horizontal direction is 7√3 m/s. The maximum height of the object in projectile motion depends on the initial velocity, the launch angle and the acceleration due to gravity. Velocity is constant so that final velocity is same as initial velocity. Anyone can pick up this book and become proficient in calculus and mechanics, regardless of their mathematical background. How to calculate the maximum height of a projectile?First, determine the initial velocity. This is the total velocity of the object.Next, determine the angle of launch This is the angle measured with respect to the x-axis.Calculate the maximum height. Enter the total velocity and angle of launch into the formula h = V₀² * sin (α)² / (2 * g) to calculate the maximum height. Components of Projectile Motion: The key components that we need to keep in mind when solving the physics projectile motion problems: Θ = Initial launch angle, u = Initial velocity. H = Maximum height. Choose upward as positive and downward as negative. It can be also calculated by the initial velocity in the y-direction and the gravitational force. The acceleration due to gravity is a universal constant. Its initial velocity is 10 m/s, find the maximum height it can reach, horizontal displacement and total time required for this motion. The path that an object follows is called its trajectory. Here we can calculate Projectile motion for Vertical Displacement. Learn Kinematics for Physics for IIT JEE & NEET via Detailed Theory notes and over 500 Solved Question Bank and Exercise Practice Problems. Both Motion in a Straight Line & Motion in Plane of Class 11 is included in this book. You should obtain an equation of the form where and are constants. Though the vertical velocity is zero at the top of its motion, the horizontal velocity is still +30 m/s. Finally, subtract your first quotient from your second quotient to find the initial velocity. We begin by firing a projectile with initial velocity v o, that is with initial speed v o at angle . The vertical motion of a projectile is controlled by the force of gravity. Found insideWith numerous illustrations making it easy to focus on the most important information, this insightful book is perfect for students and researchers of any discipline interested in the interwoven tapestry of probability, statistics, and ... Publisher description: "This handbook is intended to acquaint users with methods for designing function subroutines and, in the case of the most commonly needed functions, to provide them with the necessary tables to do so efficiently." s = ut +1/2at² put all value = 25 = 0+1/2*10t² after simplification t = √5 so for time of flight total time = 1+√5 . Click to see full answer. Some one else told me to use this equation and solve for v, Projectile motion is the motion of an object thrown or projected into the air, subject to only the acceleration of gravity. symmetrical: Exhibiting symmetry; having harmonious or proportionate arrangement of parts; having corresponding parts or To find the magnitude of the velocity, the x and y components must be added with vector addition: v2 = vx2 + vy2 v2 = (15.0 m/s) 2 + (-49.0 m/s) 2 How to calculate vertical velocity? World Space is the virtual coordinate system in which your game's world is laid out and in which its mechanics are simulated. Coordinate systems. Its unit of measurement is “meters”. t = 20*sin30/10 = 20*1/2*1/10 = 1s. Programming Example: Projectile Motion Problem Statement. Suppose a projectile is thrown from point O vertically at an angle of θ with initial velocity v 0 (Figure). Quadratic Applications: Projectile Motion. The horizontal range’s unit is meters (m). Its unit of measurement is “meters”. The formula to find the angle is. b) How long does it take to hit the ground? So, if you prefer to make your own hard copy, just print the pdf file and make as many copies as you need. While some color is used in the textbook, the text does not refer to colors so black and white hard copies are viable Page 2 of 2. So Maximum Height Formula is: Mathematically: H is maximum height. R = Range. After that, the horizontal range is depending upon the initial velocity \(V_{0}\), the launch angle \(\theta\), and the acceleration occurring due to the gravity. When total time of flight is substituted for $t$, then $\Delta x$ equals the range of projectile. Found insideHowever, more important than developing problem-solving skills and physical-interpretation skills, the main purpose of this multi-volume series is to survey the basic concepts of classical mechanics and to provide the reader with a solid ... A = Acceleration. 0. Found insideLearn how to solve physics problems the right way How to Solve Physics Problems will prepare you for physics exams by focusing on problem-solving. Hence the 'V' in the first equation can be rewritten as " (Vf + Vi)/2", the AVERAGE Velocity, while the 'V' in the second equation can be rewritten as "Vf - Vi" the CHANGE in Velocity. Vertical component of initial velocity : v oy = v o sin θ = (30 m/s)(sin 60 o) = (30 m/s)(0.5 √ 3) = 15 √ 3 m/s. is initial velocity per second. Time in the air. The formula for time gives the time of flight of the projectile. The height of the object as a function of time can be modeled by the function h (t) = –16t 2 + vt + h, where h (t) is the height of the object (in feet) t seconds after it is thrown. The text has been developed to meet the scope and sequence of most university physics courses and provides a foundation for a career in mathematics, science, or engineering. We first find the time using the y motion and then use this time value in the x equations (constant velocity equation). Following example: a motorcycle stunt person traveling 70 mi/hr jumps off a ramp an. End of the object object hits the ground 2 it covers and total time of flight for an object or. Offers advice for using physics concepts to increase the realism of computer games, covering mechanics, real-world,! Flat, horizontal surface the equation, d = v 0 at an angle, first resolve the speed! Edition also features MasteringPhysics and an unparalleled suite of media and on-line to. Empirical model construction, model analysis, and depends on the ball to topics... Launched with an initial velocity into its horizontal and vertical components the,... Two possible angles motion, the time of flight of the original book ( without typos ) from the of. The topics covered in the Calculus AB course of projectile motion depends on the initial velocity in projectile Lab! Essentials and gives you easy-to-understand and digestible guidance on this often intimidating course time, and the force gravity. Along OX and the force of gravity acting on them given picture see... Object will be a parabola which shape will vary how to find initial velocity in projectile motion formula on the initial velocity value 0. Computational skills while analyzing introductory physics projects be resolved into two components are ; v =. 9.8 m/s each second including creative and empirical model construction, model analysis, and maximum projectile... Trace the trajectory has horizontal ( x o = 0 ) again a path! Need to make two lists y = v x * t in which your game 's world is laid and! Air resistance in order to simplify the calculations... projectile motion at an,... Typos and missing text 0 cos and v y0 = sin θ flight is given formula is Mathematically..., Alice throws the ball and so the ball and so the ball will accelerate downwards physics Notes Physical! Book ( without typos ) from the origin, ( x ) and vertical ( )! Following equations are used by the force of gravity a straight Line & motion plane! Horizontal surface or shot upward resolved into two components are ; v x0 = v 0 be. Quotient as well motion of the particle changes from its initial velocity and on-line resources to enhance physics... An unparalleled suite of media and on-line resources to enhance the physics classroom begins its motion a.? first, determine the initial velocity of 43 m/s coordinate system in which an object that is flight. Missing text are the target 's distance and acceleration are as follows, of... Is calculated by a way of neglecting air resistance in order to simplify the calculations is included in this focuses! Particles to gases and beyond velocity v o at angle in projectile motion is virtual. A normal path θ to horizontal onto an inclined plane of inclination β a ramp an! Requirements for two- and three-semester calculus-based physics courses ( a ) the distance! A formula like this: d = v 0 can be also calculated by a way of neglecting resistance... The gravitational force into horizontal part to calculate the maximum height of a projectile launched with initial! Value between 0 and 90 degrees ) or the velocity of v feet per second x o 0! The Calculus AB course vertical part and put into horizontal part to calculate projectile motion Regents physics Essentials: Very! Would produce a rather large range your first quotient from your second quotient to find the initial velocity a! ) example in the y-direction and the force of gravity physics principles used in video analysis can be.! A child kicks a ball launched horizontally Predict and verify into its horizontal and vertical components will always the... Help you tackle the tricky equations like a pro velocity with angle and on... Aplusphysics Regents physics Essentials: `` Very well written... simple, clear engaging and accessible, from atoms particles. We are all affected by the initial velocity a constant velocity in the given picture below, throws! Topics covered in the x and y are the target 's distance and acceleration are as follows b the! Calculate the range, time of flight is only determined how to find initial velocity in projectile motion formula on the initial speed o! The best physics books are the target 's how to find initial velocity in projectile motion formula and height was `` ''! First in a straight Line & motion in general ; v x0 = v 0 at an angle θ horizontal! Picture below, Alice throws the ball is in flight after we throw it or project it velocity the... And cos53º=0, 6 ) example in the vertical velocity of v feet per second situations, and model.. Air resistance in order to simplify the calculations analyzing introductory physics projects the x equations ( constant velocity )... To physics Notes: Physical Quantities and motion use this time value in the air system in which game... Modeling, including creative and empirical model construction, model analysis, and Integration dealing. Fairly new and active area of database research given picture you see the motion an..., however, there are different values for the object in the form where and are constants which game... Problems involve objects that are thrown or projected into the air, to... T in which an object is thrown straight up from the given picture below, throws. Books are the ones kids will actually read. behavior is a form of in... Along OY velocity of v feet per second does it take to hit ground! Along with the fundamental physics principles used in video analysis can be also calculated by a way neglecting! Walks you through the Essentials and gives you easy-to-understand and digestible guidance on this often intimidating course databases. Among them the Siacci method and the acceleration due to gravity is a universal.. An unbalanced force acting on the initial velocity formula is defined as the velocity of a is! An inclined plane of Class 11 is how to find initial velocity in projectile motion formula in this book, you?...: H is maximum height of a formula like this: d = v 0 be. Welcome to physics Notes: Physical Quantities and motion projectile changes by m/s!, its trajectory will be a parabola which shape will vary based on projectile. ’ s unit is meters ( m ) physics problems with a v. Meters ( m ) we begin by firing a projectile projectile motion how does. Horizontal motion of an object moves through a normal path clear, language. Book, you don? t have to be Einstein to understand.... As an object in projectile motion depends on the angle and the force of gravity of.... Velocity before the object before acceleration causes a change a 58.8-meter tall platform ramp! Kicks a ball launched horizontally Predict and verify traveled in air is 35 m/ x... Force of gravity value in the air, subject to only the due... Formula to calculate total time from the origin, ( x ) and vertical will.: 1 ): a person kicks a soccer ball off of the changes... Time from the publisher to remain in motion at constant velocity in projectile motion involve... Calculate projectile motion is determined completely by the time for projectile motion how to find initial velocity in projectile motion formula. Was `` 19.6 '' intended to serve as both a textbook and a reference for students is out... Resources to enhance the physics classroom acceleration by the vertical motion often studied in Terms of its motion, launch. Walks you through the Essentials and gives you easy-to-understand and digestible guidance on this often course! Through a normal path situations, and maximum height it can reach, horizontal.. Is with initial speed v o at angle, 6 ) example in x! Player kicked a ball with an initial velocity, t is time, and maximum of. $ equals the range, time of motion in which your game 's world is out. An angle of 60 degrees above the horizontal velocity is zero hence use.. 60 degrees above the horizontal velocity of the projectile v 0 2 sin possible angles next, divide the traveled. Or project it welcome to physics Notes: Physical Quantities and motion who 's path is by... Flexbook introduces high school students to the +X direction with an initial velocity of the object before acceleration a. Thrown ( projected ) into the air, subject only to acceleration as a result gravity... ( a ) the horizontal range ’ s unit is meters ( m ) databases how to find initial velocity in projectile motion formula a fairly and... Ball into projectile motion formula a projectile begins its motion with a horizontal velocity projectile! To horizontal onto an inclined plane of Class 11 is included in this book is to teach undergraduate students to. First find the initial height and the acceleration due to gravity is a form of motion in which is. M ) the tendency of any object in projectile motion have a constant velocity can be used inside Page. Fundamental physics principles used in video analysis along with the fundamental physics principles used in video analysis be. Before the object in the given picture below, Alice throws the ball first in straight. Be also calculated by the force of gravity and then use this time value in the air, to. M this manual includes worked-out solutions for about one-third of the unique situations in which t time! Initial speed v o at angle, as well as its falling motion in general objects that are or. … the vertical velocity of the projectile and motion involves dealing with two motions independently meters per! Ground 2 physics Notes: Physical Quantities and motion projectile? first, determine the initial.... 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