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Unformatted text preview: Module-8: Motion in Two and Three Dimension Projectile is a body thrown with an initial velocity in the vertical plane and then it moves in two dimensions under the action of gravity alone without being propelled by any engine or fuel. Its motion is called projectile motion.The path of a projectile is called its trajectory. Gravity, being a downward force, causes a projectile to accelerate in the downward direction. The force of gravity could never alter the horizontal velocity of an object since perpendicular components of motion are independent of each other. A vertical force does not effect a horizontal motion. The result of a vertical force acting upon a horizontally moving object is to cause the object to deviate from its otherwise linear path. This is depicted in the animation below Examples: 1. A packet released from an airplane in flight. 2. A golf ball in flight. 3. A bullet fired from a rifle. 4. A jet of water from a hole near the bottom of a water tank. Projectile motion is a case of two-dimensional motion .Any case of two dimensional motion can be resolved into two cases of one dimensional motion -one along the x-axis and the other along the y-axis.The two cases can be studied separately as two cases of one dimensional motion.The results from two cases can be combined using vector algebra to see the net result A body can be projected in two ways : 1. Horizontal projection-When the body is given an initial velocity in the horizontal direction only. 2. Angular projection-When the body is thrown with an initial velocity at an angle to the horizontal direction. We will study the two cases separately. We will neglect the effect of air resistance. We will take x-axis along the horizontal direction and y-axis along the vertical direction. Case 1: Horizontlal Projection A body is thrown with an initial velocity u along the horizontal direction.We will study the motion along x and y axis separately.We will take the starting point to be at the origin. Case 2: Angular Projection We will now consider the case when the object is projected with an initial velocity u at an angle to the horizontal direction. We assume that there is no air resistance .Also since the body first goes up and then comes down after reaching the highest point , we will use the Cartesian 1 convention for signs of different physical quantities. The acceleration due to gravity 'g' will be negative as it acts downwards . We will separate the motion into horizontal motion (motion along x-axis) and vertical motion (motion along y- axis) .We will study x-motion and y-motion separately. Given the original conditions with which the projectile is thrown we will proceed to find the components of the original velocity and then move on to answer the following questions: • Path (trajectory) of the Projectile • How much time passes till the projectile is at the top of its flight?...
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This note was uploaded on 01/27/2012 for the course CSE 1101 taught by Professor Drmamannan during the Spring '11 term at American Intl. University.
- Spring '11