1 / 32

Projectile Motion

Projectile Motion. Chapter 3.3. Objectives. Recognize examples of projectile motion Describe the path of a projectile as a parabola Resolve vectors into their components and apply the kinematic equations to solve problems involving projectile motion. Projectile Motion.

anoki
Download Presentation

Projectile Motion

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript


  1. Projectile Motion Chapter 3.3

  2. Objectives • Recognize examples of projectile motion • Describe the path of a projectile as a parabola • Resolve vectors into their components and apply the kinematic equations to solve problems involving projectile motion

  3. Projectile Motion • How can you know the displacement, velocity and acceleration of a ball at any point in time during its flight? • Use the kinematic equations of course! 

  4. Vector Components p.98 (Running vs Jumping) While running, the person is only moving in one dimension Therefore, the velocity only has one component. V While jumping, the person is moving in two dimensions Therefore, the velocity has two components. Vy Vx

  5. Definition of Projectile Motion • Objects that are thrown or launched into the air and are subject to gravity are called projectiles • Examples? • Thrown Football, Thrown Basketball, Long Jumper, etc

  6. Path of a projectile • Neglecting air resistance, the path of a projectile is a parabola • Projectile motion is free fall with an initial horizontal velocity • At the top of the parabola, the velocity is not 0!!!!!!

  7. Vertical and Horizontal Motion

  8. Equations for projectiles launched horizontally

  9. Revised Kinematic Eqns for projectiles launched horizontally

  10. V Vy Vx Finding the total velocity • Use the pythagorean theorem to find the resultant velocity using the components (Vx and Vy) • Use SOH CAH TOA to find the direction

  11. Example p. 102 #2 • A cat chases a mouse across a 1.0 m high table. The mouse steps out of the way and the cat slides off the table and strikes the floor 2.2 m from the edge of the table. What was the cat’s speed when it slid off the table? What is the cat’s velocity just before it hits the ground?

  12. Vx= ????? What do we know and what are we looking for? Δx= 2.2 m Δy= -1.0m (bc the cat falls down) What are we looking for?? 1.0 m 2.2m

  13. How do we find Vx? • Equation for horizontal motion: • We have x…so we need t. • How do we find how long it takes for the cat to hit the ground? • Use the vertical motion kinematic equations.

  14. Vertical Motion • Δy= -1.0m • a=-9.81 m/s^2 • What equation should we use? • Rearrange the equation, to solve for t then plug in values.

  15. Horizontal equation • Rearrange and solve for Vx: • Cat’s Speed is 4.89 m/s

  16. Cliff example • A boulder rolls off of a cliff and lands 6.39 seconds later 68 m from the base of the cliff. • What is the height of the cliff? • What is the initial velocity of the boulder? • What is the velocity of the boulder just as it strikes the ground?

  17. How high is the cliff? • Δy= ? a=-9.81 m/s2 • t = 6.39 s Vx=? • Vy,i = 0 Δx= 68 m The cliff is 200 m high

  18. What is the initial velocity of the boulder? • The boulder rolls off the cliff horizontally • Therefore, we are looking for Vx

  19. Important Concepts for Projectiles Launched Horizontally

  20. Vi Vi = Vx Vy,i θ Vx,i Projectiles Launched at An Angle

  21. Vi Vy,i θ Vx,i Components of Initial Velocity for Projectiles Launched at an angle

  22. Revise the kinematic equations again

  23. Example p. 104 #3 • A baseball is thrown at an angle of 25° relative to the ground at a speed of 23.0 m/s. If the ball was caught 42.0 m from the thrower, how long was it in the air? How high was the tallest spot in the ball’s path?

  24. 25° 42.0 m What do we know?

  25. What can we use to solve the problem? Find t using the horizontal eqn: Δx=vxΔt = vicos(θ)t • How to find Δy? • Vy,f = 0 at top of the ball’s path • What equation should we use?

  26. Cliff example • A girl throws a tennis ball at an angle of 60°North of East from a height of 2.0 m. The ball’s range is 90 m and it is in flight for 6 seconds. • What is the initial horizontal velocity of the ball? • What is the initial vertical velocity of the ball? • What is the total initial velocity of the ball? • How high above the initial position does the ball get? • What is the vertical velocity of the ball 2 seconds after it is thrown?

  27. What is the initial horizontal velocity of the ball? • Δx= 90 m • Θ=60° • Total time= 6 s • Horizontal velocity is constant: Vx

  28. Vi Vy,i θ Vx,i What is the initial vertical velocity of the ball?

  29. Vi Vy,i θ Vx,i What is the total initial velocity of the ball?

  30. How high above the ground does the ball get? • At the top of the parabola, Vy is 0…so use the revised kinematic equations • Add 2m to get the height above the ground: 36.65 m

  31. What is the vertical velocity of the ball 2 seconds after it is thrown? • Vy,i=+26 m/s • a= -9.81 m/s2 • t = 2 seconds

  32. Important Concepts for Projectiles Launched at an Angle • At the top of the parabola, neither the object’s velocity nor it’s acceleration is 0!!!!! • Only Vy is 0 • Vx is constant throughout the flight • Horizontal acceleration is always 0 • Vertical acceleration is always -9.81 m/s2

More Related