Physics projectile motion

Physics projectile motion

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  PROJECTILE MOTION Sonia
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  Content Definition ofProjectile Definition of Projectile Motion Types of Projectile Motion Examples of Projectile motion Derivation of projectile motion in 2-D Factors Affecting Projectile Motion
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  Definition Of Projectile A projectile is any object that once projected or dropped continues in motion by its own inertia and 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, the free-body diagram of a projectile would show a single force acting downwards and labeled force of gravity (or simply Fgrav). Regardless of whether a projectile is moving downwards, upwards, upwards and rightwards, or downwards and leftwards, the free-body diagram of the projectile is still as depicted in the diagram at the right. Fgrav Free-body diagram of a projectile
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  Definition Of Projectile Motion Projectile motion is a form of motion in which an object or particle (called a projectile) is thrown near the earth's surface, and it moves along a curved path under the action of gravity only. Example: Parabolic water trajectory
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  Types Of ProjectileMotion • Horizontal – Motion of a ball rolling freely along a level surface – Horizontal velocity is ALWAYS constant • Vertical – Motion of a freely falling object – Force due to gravity – Vertical component of velocity changes with time • Parabolic – Path traced by an object accelerating only in the vertical direction while moving at constant horizontal velocity
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  Examples Of ProjectileMotion Launching a Cannon ball
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  Examples Of ProjectileMotion Object thrown upward from a car moving in a horizontal direction
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  Derivation Of ProjectileMotion in 2-D The initial velocity If the projectile is launched with an initial velocity , then it can be written as The components and can be found if the angle, is known: If the projectile's range, launch angle, and drop height are known, launch velocity can be found using Newton's formula The launch angle is usually expressed by the symbol theta, but often the symbol alpha is used. Initial velocity of parabolic throwing Components of initial velocity of parabolic throwing
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  Derivation Of ProjectileMotion in 2-D Kinematic quantities of projectile motion In projectile motion, the horizontal motion and the vertical motion are independent of each other; that is, neither motion affects the other. Acceleration Since there is no acceleration in the horizontal direction, the velocity in the horizontal direction is constant, being equal to The vertical motion of the projectile is the motion of a particle during its free fall. Here the acceleration is constant, being equal to The components of the acceleration are:
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  Derivation Of ProjectileMotion in 2-D Velocity The horizontal component of the velocity of the object remains unchanged throughout the motion. The vertical component of the velocity increases linearly, because the acceleration due to gravity is constant. The accelerations in the and directions can be integrated to solve for the components of velocity at any time , as follows: The magnitude of the velocity (under the Pythagorean theorem):
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  Derivation Of ProjectileMotion in 2-D Displacement Displacement and coordinates of parabolic throwing At any time , the projectile's horizontal and vertical displacement: The magnitude of the displacement: Displacement and coordinates of parabolic throwing
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  Derivation Of ProjectileMotion in 2-D Parabolic trajectory Consider the equations, If t is eliminated between these two equations the following equation is obtained: This equation is the equation of a parabola. Since , and are constants, the above equation is of the form in which a and b are constants. This is the equation of a parabola, so the path is parabolic. The axis of the parabola is vertical.
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  Derivation Of ProjectileMotion in 2-D The maximum height of projectile The highest height which the object will reach is known as the peak of the object's motion. The increase of the height will last, until that is, Time to reach the maximum height: From the vertical displacement of the maximum height of projectile: Maximum height of projectile
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  Derivation Of ProjectileMotion in 2-D The maximum distance of projectile It is important to note that the Range and the Maximum height of the Projectile does not depend upon mass of the trajected body. Hence Range and Maximum height are equal for all those bodies which are thrown by same velocity and direction. Air resistance does not affect displacement of projectile. The horizontal range d of the projectile is the horizontal distance the projectile has travelled when it returns to its initial height (y = 0). Maximum distance of projectile
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  Derivation Of ProjectileMotion in 2-D Time to reach ground: From the horizontal displacement the maximum distance of projectile: So Note that d has its maximum value when which necessarily corresponds to Maximum distance of projectile
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  Factors Affecting Projectile Motion What two factors would affect projectile motion? – Angle – Initial velocity Initial Velocity Angle
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