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Projectile Motion: Understanding Motion in Two Dimensions

Learn about projectile motion, a type of motion in which an object moves in both the x and y directions simultaneously under the influence of Earth's gravity. This chapter discusses the assumptions, rules, and problem-solving strategies for projectile motion.

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Projectile Motion: Understanding Motion in Two Dimensions

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  1. Chapter 6 Two-Dimensional Motion

  2. Motion in Two Dimensions • Using + or – signs is not always sufficient to fully describe motion in more than one dimension • Vectors can be used to more fully describe motion • Still interested in displacement, velocity, and acceleration

  3. Projectile Motion • An object may move in both the x and y directions simultaneously • It moves in two dimensions • The form of two dimensional motion we will deal with is called projectile motion

  4. Projectile Motion A projectile is an object moving in two dimensions under the influence of Earth's gravity; its path is a parabola.

  5. Assumptions of Projectile Motion • We may ignore air friction • We may ignore the rotation of the earth • With these assumptions, an object in projectile motion will follow a parabolic path

  6. Rules of Projectile Motion • The x- and y-directions of motion are completely independent of each other • The x-direction is uniform motion • ax = 0 • The y-direction is free fall • ay = -g • The initial velocity can be broken down into its x- and y-components

  7. Projectile Motion

  8. Projectile Motion at Various Initial Angles • Complementary values of the initial angle result in the same range • The heights will be different • The maximum range occurs at a projection angle of 45o

  9. Some Details About the Rules • x-direction • ax = 0 • x = vxot • This is the only operative equation in the x-direction since there is uniform velocity in that direction

  10. The y-Direction

  11. More Details About the Rules • y-direction • free fall problem • a = -g • take the positive direction as upward • uniformly accelerated motion, so the motion equations all hold

  12. Velocity of the Projectile • The velocity of the projectile at any point of its motion is the vector sum of its x and y components at that point • Remember to be careful about the angle’s quadrant

  13. Problem-Solving Strategy • Select a coordinate system and sketch the path of the projectile • Include initial and final positions, velocities, and accelerations • Resolve the initial velocity into x- and y-components • Treat the horizontal and vertical motions independently

  14. Problem-Solving Strategy, cont • Follow the techniques for solving problems with constant velocity to analyze the horizontal motion of the projectile • Follow the techniques for solving problems with constant acceleration to analyze the vertical motion of the projectile

  15. Some Variations of Projectile Motion • An object may be fired horizontally • The initial velocity is all in the x-direction • vo = vx and vy = 0 • All the general rules of projectile motion apply

  16. Non-Symmetrical Projectile Motion • Follow the general rules for projectile motion • Break the y-direction into parts • up and down • symmetrical back to initial height and then the rest of the height

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