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Kinematics Geometry of Motion

Kinematics Geometry of Motion. What is Kinematics?. Kinematics is the study of the geometry of motion and is used to relate displacement, velocity, acceleration and time without reference to the cause of motion. or. Projectile Motion Assumptions.

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Kinematics Geometry of Motion

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  1. Kinematics Geometry of Motion

  2. What is Kinematics? Kinematics is the study of the geometry of motion and is used to relate displacement, velocity, acceleration and time without reference to the cause of motion.

  3. or Projectile Motion Assumptions • The variations of gravity (g) with respect to differing altitudes is negligible and can be ignored. • Gravity is constant:

  4. Projectile Motion First step: To analyze projectile motion, separate the two-dimensional motion into vertical and horizontal components.

  5. Projectile Motion Horizontal Direction, x, represents the range, or distance the projectile travels. Vertical Direction, y, represents the altitude, or height, the projectile reaches.

  6. Projectile Motion Formulas Initial Velocity (vi) can be broken down into its x and y components:

  7. Projectile Motion Formulas Going one step further: There is a right triangle relationship between the velocity vectors – Use Right Triangle Trigonometry to solve for each of them.

  8. 90° θ° Right Triangle Review: • Right triangle: • A triangle with a 90° angle. Hypotenuse, H Opposite side, O Sides: Hypotenuse, H Adjacent side, A Opposite side, O Adjacent side, A

  9. Trigonometric Functions: • Trigonometric Functions: • sin θ° = O / H • cos θ° = A / H • tan θ° = O / A

  10. Projectile Motion Problem • A ball is fired from a device, at a rate of 160 ft/sec, with an angle of 53 degrees to the ground.

  11. Projectile Motion Problem • Find the x and y components of Vi. • At the highest point (the vertex) what is the altitude (h) and how much time has elapsed? • What is the ball’s range (the distance traveled horizontally)?

  12. Projectile Motion Problem Find the x and y components of Vi. Vi = initial velocity = 160 ft/sec

  13. Projectile Motion Problem Find the x and y components of Vi.

  14. Projectile Motion Problem Find the x and y components of Vi.

  15. Projectile Motion Problem At the highest point (the vertex), what is the altitude (h) and how much time has elapsed?Start by solving for time.

  16. Projectile Motion Problem At the highest point (the vertex), what is the altitude (h) and how much time has elapsed?Now using time, find h (ymax).

  17. Projectile Motion Problem What is the ball’s range (the distance traveled horizontally)? It takes the ball the same amount of time to reach its maximum height as it does to fall to the ground, so total time (t) = 8 sec. Using the formula:

  18. Projectile Motion Problem-2 A golf ball is hit at an angle of 37 degrees above the horizontal with a speed of 34 m/s. What is its maximum height, how long is it in the air, and how far does it travel horizontally before hitting the ground?

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