1 / 36

Introduction to Projectile Motion

Introduction to Projectile Motion. Mr. Chin-Sung Lin. Introduction to Projectile Motion. What is Projectile Motion?. Trajectory of a Projectile. Calculation of Projectile Motion. Introduction to Projectile Motion. What is Projectile Motion?. Trajectory of a Projectile.

marcena-terence
Télécharger la présentation

Introduction to 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. Introduction toProjectile Motion Mr.Chin-Sung Lin

  2. Introduction to Projectile Motion • What is Projectile Motion? • Trajectory of a Projectile • Calculation of Projectile Motion

  3. Introduction to Projectile Motion • What is Projectile Motion? • Trajectory of a Projectile • Calculation of Projectile Motion

  4. What is Projectile Motion?

  5. Features of Projectile Motion? Thrown into the Air 2-D Motion Parabolic Path Affected by Gravity Determined by Initial Velocity

  6. Definition: Projectile Motion Projectile motion refers to the 2-D motion of an object that is given an initial velocity and projected into the air at an angle. The only force acting upon the object is gravity. It follows a parabolic path determined by the effect of the initial velocity and gravitational acceleration.

  7. Definition: Projectile Motion Projectile motion refers to the 2-D motion of an object that is given an initial velocity and projected into the air at an angle. The only force acting upon the object is gravity. It follows a parabolic path determined by the effect of the initial velocity and gravitational acceleration.

  8. Introduction to Projectile Motion • What is Projectile Motion? • Trajectory of a Projectile • Calculation of Projectile Motion

  9. Trajectory (Path) of a Projectile

  10. Trajectory (Path) of a Projectile

  11. y v0 x

  12. y x

  13. y x

  14. y x

  15. y • Velocity is changing and the motion is accelerated • The horizontal component of velocity (vx) is constant • Acceleration from the vertical component of velocity (vy) • Acceleration due to gravity is constant, and downward • a = - g = - 9.81m/s2 g = 9.81m/s2 x

  16. y • The horizontal and vertical motions are independent of each other • Both motions share the same time (t) • The horizontal velocity ....vx = v0 • The horizontal distance .... dx = vx t • The vertical velocity ........ vy = - g t • The vertical distance ........ dy = 1/2 gt2 g = 9.81m/s2 x

  17. Trajectory (Path) of a Projectile • The path of a projectile is the result of the simultaneous effect of the H & V components of its motion • H component  constant velocity motion • V component  accelerated downward motion • H & V motions are independent • H & V motions share the same time t • The projectile flight time t is determined by the V component of its motion

  18. Trajectory (Path) of a Projectile • H velocity is constant vx = v0 • V velocity is changing vy = - g t • H range: dx = v0 t • V distance: dy = 1/2 gt2

  19. Introduction to Projectile Motion • What is Projectile Motion? • Trajectory of a Projectile • Calculation of Projectile Motion

  20. v0 d g t R Calculation of Projectile Motion • Example: A projectile was fired with initial velocity v0horizontally from a cliff d meters above the ground. Calculate the horizontal range R of the projectile.

  21. v0 d g t R Strategies of Solving Projectile Problems • H & V motions can be calculated independently • H & V kinematics equations share the same variable t

  22. v0 d g t R Strategies of Solving Projectile Problems H motion: dx = vx t R = v0 t V motion: dy = d = 1/2 gt2 t =sqrt(2d/g) So, R = v0 t = v0 * sqrt(2d/g)

  23. Numerical Example of Projectile Motion H motion: dx = vx t R = v0 t = 10 t V motion: dy = d = 1/2 gt2 t =sqrt(2 *19.62/9.81) = 2 s So, R = v0 t = v0 * sqrt(2d/g) = 10 * 2 = 20 m V0 = 10 m/s g = 9.81 m/s2 19.62 m t R

  24. V0 = 10 m/s g = 9.81 m/s2 d t 20 m Exercise 1: Projectile Problem A projectile was fired with initial velocity 10 m/s horizontally from a cliff. If the horizontal range of the projectile is 20 m, calculate the height d of the cliff.

  25. V0 = 10 m/s g = 9.81 m/s2 d t 20 m Exercise 1: Projectile Problem H motion: dx = vx t 20 = v0 t = 10 t t = 2 s V motion: dy = d = 1/2 gt2 = 1/2 (9.81)22 = 19.62 m So, d = 19.62 m

  26. V0 g = 9.81 m/s2 19.62 m t 20 m Exercise 2: Projectile Problem A projectile was fired horizontally from a cliff 19.62 m above the ground. If the horizontal range of the projectile is 20 m, calculate the initial velocity v0 of the projectile.

  27. V0 g = 9.81 m/s2 19.62 m t 20 m Exercise 2: Projectile Problem H motion: dx = vx t 20 = v0 t V motion: dy = d = 1/2 gt2 t =sqrt(2 *19.62/9.81) = 2 s So, 20 = v0 t = 2 v0 v0 = 20/2 = 10 m/s

  28. Summary of Projectile Motion • What is Projectile Motion? • Trajectory of a Projectile • Calculation of Projectile Motion

  29. Projectile Motion with Angles Mr.Chin-Sung Lin

  30. Example: Projectile Problem – H & V A projectile was fired from ground with 20 m/s initial velocity at 60-degree angle. What’s the horizontal and vertical components of the initial velocity? g = 9.81 m/s2 20 m/s vy 60o vx

  31. Example: Projectile Problem – At the Top A projectile was fired from ground with 20 m/s initial velocity at 60-degree angle. What’s the velocity of the projectile at the top of its trajectory? v g = 9.81 m/s2 20 m/s vy t 60o vx R

  32. Example: Projectile Problem – Height A projectile was fired from ground with 20 m/s initial velocity at 60-degree angle. What’s the maximum height that the ball can reach? g = 9.81 m/s2 20 m/s vy h 60o vx

  33. Example: Projectile Problem - Time A projectile was fired from ground with 20 m/s initial velocity at 60-degree angle. How long will the ball travel before hitting the ground? g = 9.81 m/s2 20 m/s vy t 60o vx

  34. Example: Projectile Problem – H Range A projectile was fired from ground with 20 m/s initial velocity at 60-degree angle. How far will the ball reach horizontally? g = 9.81 m/s2 20 m/s vy 60o vx R

  35. Example: Projectile Problem – Final V A projectile was fired from ground with 20 m/s initial velocity at 60-degree angle. What’s the final velocity of the projectile right before hitting the ground? g = 9.81 m/s2 20 m/s vy 60o vfx vx vfy vf

  36. Example: Projectile Problem – Max R A projectile was fired from ground with 20 m/s initial velocity. How can the projectile reach the maximum horizontal range? What’s the maximum horizontal range it can reach? g = 9.81 m/s2 20 m/s q R

More Related