Make a Prediction

1. Make a Prediction • Below, you have two cannon balls. One is launched with a horizontal initial velocity of 10 m/s, and the other ball is dropped straight down from the top of the cliff. Which ball will hit the ground first? (In the absence of air resistance)

2. BELLWORK 11/30/17 • What is a projectile?

3. ANSWER • Any moving object upon which the only force acting on it is gravity.

4. Projectile Motion Motion In Two Dimensions We restrict ourselves to objects thrown near the Earth’s surface so that gravity can be considered constant.

5. A projectile is defined as any moving object upon which the only force acting on it is gravity. A projectile is any object that once projected or dropped continues in motion by its own inertia and is influenced only by the downward force of gravity.

6. To further investigate a downward force and a downward acceleration of a projectile, consider a cannonball shot horizontally from a very high cliff at a high speed.And suppose for a moment that the gravity switch could be turned off such that the cannonball would travel in the absence of gravity? What would the motion of such a cannonball be like? How could its motion be described?

7. Now suppose that the gravity switch is turned on and that the cannonball is projected horizontally from the top of the same cliff. Will gravity affect the cannonball's horizontal motion? Will the cannonball travel further, closer, or the same horizontal distance due to the influence of gravity? Gravity only effects its vertical motion. The ball will travel the same horizontal distance.

8. Projectile Problem • There is an interesting monkey down at the zoo. The monkey spends most of its day hanging from a limb of a tree. • The zookeeper feeds the monkey by shooting bananas from a banana cannon to the monkey in the tree. This particular monkey has a habit of dropping from the tree the moment that the banana leaves the muzzle of the cannon. • The zookeeper is faced with the dilemma of where to aim the banana cannon in order to hit the monkey. If the monkey lets go of the tree the moment that the banana is fired, should the zookeeper aim the banana above the monkey, at the monkey, or below the monkey.

9. To ponder this dilemma consider the following scenarios: Scenario 1: What would happen if you shot the banana cannon at the monkey in a gravity free environment?

10. ANSWER In the absence of gravity, the banana moves in a straight line path (and does not experience any downward acceleration) and the monkey does not fall once he lets go of the tree.

11. Scenario #2: What would happen if you shot the banana cannon above the monkey in the presence of gravity?

12. ANSWER The banana moves in a parabolic path in the presence of gravity. In the presence of gravity, the monkey also accelerates downward once he lets go of the limb. Both banana and monkey experience the same acceleration since gravity causes all objects to accelerate at the same rate regardless of their mass. Since both banana and monkey experience the same acceleration each will fall equal amounts. The banana misses the monkey, moving over his head as it was originally aimed.

13. Scenario #3: What would happen if you shot the banana cannon at the Monkey at a Fast Speed with Gravity On?

14. ANSWER Since the banana left the muzzle moving very fast, the banana reaches the monkey before the monkey has fallen very far.

15. Scenario #4: What would happen if you shot the banana cannon at the Monkey at a Slow Speed with Gravity On?

16. ANSWER Since the banana left the muzzle moving very slow, the banana reaches the monkey after the monkey has fallen considerably far.

17. So….. • Should the zookeeper aim the banana above the monkey, at the monkey, or below the monkey?

18. ANSWER • The zookeeper’s should aim the banana cannon directly at the monkey.

19. Characteristics of Projectiles • Projectile motion is a combination of horizontal motion and vertical motion. (Two- dimensional motion) • The horizontal motion of a projectile is constant because there are no horizontal forces acting on it other than its initial velocity. • Therefore; Vi = Vf

20. The vertical motion of a projectile is nothing more than free fall with a constant downward acceleration due to gravity. (We are neglecting air resistance)

21. The path of a projectile is called its trajectory. The trajectory of a projectile in free fall is a parabola.

22. A projectile, once projected, continues in motion by its own inertia and is influenced only by the downward force of gravity.

24. Projectile Equations – We can use our Kinematic Equations from Ch.2 Horizontal Motion Vertical Motion Vf = aΔt Vf2 = 2aΔy Δy = 1/2a(Δt)2 • Δx = ViΔt • Vi = Vf = Constant .

25. Classwork – Horizontally Launched Projectiles • Complete #’s 1-4 on Page 99 • Add Chapter 3 Formulas to index card. Use Page 854 in book.

26. Projectile Motion Review

27. Question #1: Explain why an object projected horizontally will reach the ground in the same amount of time as an object dropped vertically.

28. ANSWER • Because gravity is pulling both projectiles downward at the same rate.

29. Question #2: Why does the horizontal velocity of a projectile’s motion remain constant?

30. ANSWER • Because there are no horizontal forces acting on it. • There are no horizontal forces speeding it up or slowing it down.

31. Question #3: Why does the vertical velocity of a projectile’s motion undergo change?

32. ANSWER • Because the force of gravity is acting on the projectile, and increasing its velocity.

33. Question #4: What is a projectile?

34. ANSWER • A moving object in which the only force acing on it is the force of gravity

35. Question #5 • A marble rolling across a desk with an initial velocity of 0.57m/s, falls 1.5 m from the desk to the floor. How far from the base of the desk will the marble land?

36. Projectiles Launched at an Angle • Complete the PHET Lab Simulation

37. Projectiles Launched at An Angle Maximum range is achieved if the projectile is fired at an angle of_____ degrees with respect to the horizontal.