Projectile Motion

AcknowledgementI thank my dear teachers to give such a wonderful topic and my institution for giving me such wonderful opportunities.I would also like to thank my parents for supporting me throughout the project.

Page 21 of 22

IndexSr no.Page No.

1. Introduction3

2. History of Projectile Motion5

3. Horizontally Launched Projectiles8

4. Non-Horizontally Launched Projectiles10

5. Applications13

6. Our Investigation17

7. Conclusion19

8. Bibliography20

9. Remarks22

IntroductionA projectile is an object upon which the only force acting is gravity. Projectile is any object that onceprojectedor dropped continues in motion by its owninertiaand is influenced only by the downward force of gravity. By definition, a projectile has a single force that acts upon it - the force of gravity. If there were any other force acting upon an object, then that object would not be a projectile. Thus, thefree-body diagramof a projectile would show a single force acting downwards and labelled force of gravity (or simply Fgrav). By definition, a projectile is any object upon which the only force is gravity.Projectile Motion and InertiaMany students have difficulty with the concept that the only force acting upon an upward moving projectile is gravity. Their conception of motion prompts them to think that if an object is moving upward, then theremustbe an upward force. And if an object is moving upward and rightward, theremustbe both an upward and rightward force. Their belief is that forces cause motion; and if there is an upward motion then there must be an upward force. They reason, "How in the world can an object be moving upward if the only force acting upon it is gravity?"Newton's laws suggest that forces are only required to cause an acceleration (not a motion). TheNewton's laws stood in direct opposition to the common misconceptionthat a .force is required to keep an object in motion. This idea is simplynottrue! A force isnotrequired to keep an object in motion. A force is only required to maintain an acceleration. And in the case of a projectile that is moving upward, there is a downward force and a downward acceleration. That is, the object is moving upward and slowing down.To further ponder this concept of the downward force and a downward acceleration for a projectile, consider a cannonball shot horizontally from a very high cliff at a high speed. And suppose for a moment that thegravity switchcould beturned offsuch that the cannonball would travel in the absence of gravity? What would the motion of such a cannonball be like? How could its motion be described? According toNewton's first law of motion, such a cannonball would continue in motion in a straight line at constant speed. If not acted upon by an unbalanced force, "an object in motion will continue to remain at rest or in motion until acted by an external force"Now suppose that thegravity switchis turned on and that the cannonball is projected horizontally from the top of the same cliff. What effect will gravity have upon the motion of the cannonball? Will gravity affect the cannonball's horizontal motion? Will the cannonball travel a greater (or shorter) horizontal distance due to the influence of gravity? The answer to both of these questions is "No!" Gravity will act downwards upon the cannonball to affect its vertical motion. Gravity causes a vertical acceleration. The ball will drop vertically below its otherwise straight-line, inertial path. Gravity is the downward force upon a projectile that influences its vertical motion and causes the parabolic trajectory that is characteristic of projectiles.A projectile is an object upon which the only force is gravity. Gravity acts to influence the vertical motion of the projectile, thus causing a vertical acceleration. The horizontal motion of the projectile is the result of the tendency of any object in motion to remain in motion at constant velocity. Due to the absence of horizontal forces, a projectile remains in motion with a constant horizontal velocity. Horizontal forces arenotrequired to keep a projectile moving horizontally. The only force acting upon a projectile is gravity!

History on Projectile MotionIt was Galileo who first accurately described projectile motion.He showed that it could be understood by analysing the horizontaland vertical components separately. No one had done this prior to Galileo.This illustration reflects the general opinion 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, as this illustration from a work by Niccolo Tartaglia shows, 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 motions, and these work together to create a precise mathematical curve. He actually found that the curve has an exact mathematical shape. A shape that the Greeks had already studied and called theparabola. The conclusion that Galileo reached was that the path ofanyprojectile is a parabola.

At a given location on the earth and in the absence of air resistance, all objects fall with the same uniform acceleration. Thus, two objects of different sizes and weights, dropped from the same height, will hit the ground at the same time.

An object is controlled by two independant motions. So an object projected horizontally will reach the ground in the same time as an object dropped vertically. No matter how large the horizontal velocity is, the downward pull of gravity is always the same.

Horizontally Launched ProjectilesConsider a cannonball projected horizontally by a cannon from the top of a very high cliff. In the absence of gravity, the cannonball would continue its horizontal motion at a constant velocity. This is consistent with thelaw of inertia. And furthermore, if merely dropped from rest in the presence of gravity, the cannonball would accelerate downward, gaining speed at a rate of 9.8 m/s every second. This is consistent with our conception offree-falling objectsaccelerating at a rate known as theacceleration of gravity.If our thought experiment continues and we project the cannonball horizontally in the presence of gravity, then the cannonball would maintain the same horizontal motion as before - a constant horizontal velocity. Furthermore, the force of gravity will act upon the cannonball to cause the same vertical motion as before - a downward acceleration. The cannonball falls the same amount of distance as it did when it was merely dropped from rest (refer to diagram below). However, the presence of gravity does not affect the horizontal motion of the projectile. The force of gravity acts downward and is unable to alter the horizontal motion. There must be a horizontal force to cause a horizontal acceleration. (And we know thatthere is only a vertical force acting upon projectiles.) The vertical force acts perpendicular to the horizontal motion and will not affect it sinceperpendicular components of motion are independent of each other. Thus, the projectile travels with aconstant horizontal velocityand adownward vertical acceleration.

Equation:- 1) Equation of Trajectory:a) Horizontal Equation=x=utb) Vertical Equation=y=1/2gt2This is the equation of a parabola, symmetric about y-axis. Hence the path of the projectile is parabolic.2) Time Of Descent: Time taken for the projectile to come to the earth.t= 3) Horizontal Range=X=distance travelled by the projectile in horizontal directionX=u*

Non horizontal projectile motionNow suppose that our cannon is aimed upward and shot at an angle to the horizontal from the same cliff. In the absence of gravity (i.e., supposing that thegravity switchcould beturned off) the projectile would again travel along a straight-line, inertial path. An object in motion would continue in motion at a constant speed in the same direction if there is no unbalanced force. This is the case for an object moving through space in the absence of gravity. However, if thegravity switchcould beturned onsuch that the cannonball is truly a projectile, then the object would once morefree-fallbelow this straight-line, inertial path. In fact, the projectile would travel with aparabolictrajectory. The downward force of gravity would act upon the cannonball to cause the same vertical motion as before - a downward acceleration. The cannonball falls the same amount of distance in every second as it did when it was merely dropped from rest (refer to diagram below). Once more, the presence of gravity does not affect the horizontal motion of the projectile. The projectile still moves the same horizontal distance in each second of travel as it did when thegravity switchwas turned off. The force of gravity is a vertical force and does not affect horizontal motion; perpendicular components of motion are independent of each other.

In conclusion, projectiles travel with a parabolic trajectory due to the fact that the downward force of gravity accelerates them downward from their otherwise straight-line, gravity-free trajectory. This downward force and acceleration results in a downward displacement from the position that the object would be if there were no gravity. The force of gravity does not affect the horizontal component of motion; a projectile maintains a constant horizontal velocity since there are no horizontal forces acting upon it.

Projectile Motion Formula(trajectory formula)is given by

Where Vxis the velocity along x-axis, Vxois the initialvelocity along x-axis, Vyis the velocity along y-axis, Vyois the initial velocity along y-axis. g is the acceleration due to gravity and t is the time taken.

Equations relatedtotrajectory motion (projectile motion) are given by

Where Vois the initial Velocity, sinis the component along y-axis, cosis the component along x-axis.

Projectile Motion formula is used to find the distance, velocity andtime taken in the projectile motion.

Applications of Projectile Motion1) In Sports: Cricket

Javelin throw

Rugby

Football

2) Powered Projectiles, Rockets And Missiles and Canons:Advanced military techniques include missile launching which uses projectile motion equations to calculate the distance at where the missile is going to fall. The same goes for canons, catapults, ballista, trebuchets and rockets.

Missile:-

Canons

Trebuchet:-

Fountains: - Projectile motion concept is used to determine the height of the fountain of water and the distance it will go. Its used in building fountains.

Our Investigation: Aim: - To investigate the velocity and the maximum height reached by a projectile fired at an angle made with the horizontal from the range and angle and the time period from the made model.

Apparatus: -

Observation Table: -AngleRangeR mVelocityV m/sHeightH mTimeT s

300.813.0270.1160.30

401.183.4260.2470.45

500.822.8560.2440.44

600.83.0080.3460.53

700.633.0990.4320.59

AngleSin RgSin2Sq. Root of Sin2Sq. Root of Rg

300.52940.8669.31E-019.65E-01

400.6423920.9849.92E-019.96E-01

500.7664900.9849.92E-019.96E-01

600.8665880.8669.31E-019.65E-01

700.9396860.6428.01E-018.95E-01

Result: - As the angle increases, the range of the projectile increases till 450 and then decreases till 900. The velocity component remains the same as we are stretching the rubber the same way every timeConclusionsProjectile is a very interesting topic of itself. It shows us the beauty of physics in a completely different way. It helps us calculate basic components of parabolic motion such as velocity, range and maximum height etc without the consideration of mass of the body which makes it less complicate to calculate the components.

Before this investigatory projectile was just the part of the physics book but now after knowing the applications of projectile our concepts about it are clear. By doing this project we learned to connect projectile motion to many real life situations.Bibliography

http://www.scienceclarified.com/everyday/Real-Life-Chemistry-Vol-3-Physics-Vol-1/Projectile-Motion.htmlhttp://www.physicsclassroom.com/mmedia/vectors/hlp.cfmhttp://www.physicsclassroom.com/class/vectors/u3l2e.cfmhttp://serc.carleton.edu/sp/compadre/uncertainty/examples/example5.htmlhttp://answers.yahoo.com/question/index?qid=20070519032007AAcE7UVhttp://www.scienceclarified.com/everyday/Real-Life-Chemistry-Vol-3-Physics-Vol-1/Projectile-Motion-Real-life-applications.htmlhttp://homepage.usask.ca/~dln136/projectile/pages/module5.htmlhttp://homepage.usask.ca/~dln136/projectile/pages/module3.htmlhttp://formulas.tutorvista.com/physics/projectile-motion-formula.htmlhttp://www.physicsclassroom.com/class/vectors/u3l2a.cfmhttp://en.wikipedia.org/wiki/Projectile_motionhttp://www.physicsclassroom.com/Class/vectors/U3L2b.cfmhttp://www.physicsclassroom.com/Class/vectors/U3L2c2.cfmhttp://www.physicsclassroom.com/class/vectors/U3L2e.cfmhttp://usnavymuseum.org/Education_LP0014.asp

RemarksPlease write suggestions and improvements to be made in the project.