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2-D Kinematics

2-D Kinematics. VARIABLE SOUP TEXTBOOK CH.3. Projectile Motion. This is motion that occurs in two dimensions: Horizontal motion is at constant velocity Vertical motion accelerated by gravity Mass-Independent. Projectile Motion.

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2-D Kinematics

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  1. 2-D Kinematics VARIABLE SOUP TEXTBOOK CH.3

  2. Projectile Motion • This is motion that occurs in two dimensions: • Horizontal motion is at constant velocity • Vertical motion accelerated by gravity • Mass-Independent

  3. Projectile Motion • Projectile: An object that moves through space acted on only by the earth’s gravity. Projectile moving straight out and falling down – ball off table. Projectile that starts at a given level and moves upward and downward, like a football being thrown

  4. When an object is moving in multiple directions, the motion in one dimension has no effect on motion in another dimension. • The x- and y- components areINDEPENDENT of each other. • Time is the bridge between the two components. The Law of Compound Motion

  5. Projectile Motion • Horizontal velocity is maintained by inertia • An equal distance is traveled each second • “Constant Velocity”

  6. 5 m 10 m/s 1 s Projectile Motion 20 m 20 m/s 2 s Vertical velocity increases each second with the pull of gravity in free fall. Each second the ball goes 10 m/s faster than the previous second and a greater distance. 45 m 30 m/s 3 s 80 m 40 m/s 4 s 125 m 50 m/s 5 s

  7. x – component Equations y – component Equations x = vixt + ½axt2 y = viyt + ½ayt2 vfx2 = vix2 + 2axx vfy2 = viy2 + 2ayy vfx = vix + axt vfy = viy + ayt x = ½(vix + vfx)t y = ½(viy + vfy)t Kinematics Equations

  8. Initial Velocity vs. Final Velocity • A vector, vi • What are the two parts? • What unit should we use? • vi = vix + viy vfx vi viy vf vfy vix A vector, vf Also known as impact velocity. vf= vfx + vfy

  9. Acceleration • This value is constant • What unit? • What are typical values? • a = ax + ay ax a ay

  10. Displacementr = x + y x - components y - components • Range, xf • vix • vfx • xi typically set to zero. • ax • Height, y • Maximum height, yMAX • viy • vfy • vf = velocity at time tf • vf is often the impact velocity • ay, often g, watch the sign!

  11. Conceptual Questions • If ax = 0, what happens to vx? • If y = 0, how are viy and vfy related? • What is vy at the top of a trajectory?

  12. Projectile Motion When projectiles are launched at an angle, the initial velocity has ahorizontaland averticalcomponent. v vy vx

  13. Projectile Motion The path of the cannon ball is in the shape of a parabola. The dimensions of the parabola are determined by the magnitude of thevxandvycomponents. vy vx

  14. Projectile Motion If the angle of launch is high, velocityvyis much greater than velocityvx. The cannon ball goes higher in the air, but does not go as far. vy vx

  15. Projectile Motion If the angle of launch is low, velocityvxis much greater than velocityvy. The cannon ball goes farther, but does not go as high. vy vx Try this.

  16. Projectile Motion With your new understanding of projectile motion, you can test your skill at these web sites. Archery Artillery

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