Chapter 5 Projectile Motion

1. Chapter 5 Projectile Motion Conceptual Physics Chapter 5

2. Adding Vectors Graphically • Determine a scale that is appropriate for the drawing area that you have. I will use 1 cm to represent 0.5 km of true distance. 1 cm Conceptual Physics Chapter 5

3. 0.5 km 1 cm Adding Vectors Graphically Vector A measures 2 km to the East and vector B measures 3 km to the East. Add the vectors graphically. 2 km, E · = 5 km Vector A 3 km, E East Resultant measures 10 cm Vector B Reposition the vectors with the tail of the first vector attached to the head of the second vector. The resultant vector measures from the tail of the first vector to the head of the last vector. 1 cm = 0.5 km Conceptual Physics Chapter 5

4. 0.5 km 1 cm Adding Vectors Graphically Vector A measures 2 km to the East and vector B measures 3 km to the West. Add the vectors graphically. 2 km, E · = 1 km Vector A 3 km, W Resultant measures 2 cm West Vector B The resultant vector measures from the tail of the first vector to the head of the last vector. Position the vectors head to tail 1 cm = 0.5 km Conceptual Physics Chapter 5

5. 0.5 km 1 cm Adding Vectors Graphically Vector A measures 2 km to the East and vector B measures 3 km to the North. Add the vectors graphically. 2 km, E · = 3.6 km Vector B Vector A The resultant vector measures from the tail of the first vector to the head of the last vector. Measure the angle to determine the direction of the resultant. 7.2 cm Resultant measures Position the vectors head to tail 3 km, N 34° East of North 1 cm = 0.5 km Conceptual Physics Chapter 5

6. Adding Vectors Graphically • Any number of vectors can be added together as long as they are positioned head to tail. Conceptual Physics Chapter 5

7. Adding Vectors Graphically • The resultant is always drawn from the tail of the first vector to the head of the last vector. Conceptual Physics Chapter 5

8. B D E C A Adding Vectors Graphically • The order of vector addition is unimportant. C B E D A Conceptual Physics Chapter 5

9. Vector Resolution • A single vector can be resolved into its components. • Components will always be perpendicular to one another and must add together to be equal to the original vector. Conceptual Physics Chapter 5

10. Vector Resolution Find the x and y components of the vector below. The components can then be measured to determine their magnitude These construction lines define the limits of the two component vectors Then produce a vertical construction line that passes through the head of the original vector The effect of the two component vectors is equivalent to that of the original vector Produce a horizontal construction line that passes through the tail of the original vector y component x component Conceptual Physics Chapter 5

11. Projectile Motion A projectile is any object which simultaneously moves in two dimensions under the influence of gravity. Conceptual Physics Chapter 5

12. Projectile Motion The path of the projectile is referred to as its trajectory and the shape of the path is parabolic. Conceptual Physics Chapter 5

13. Projectile Motion An arrow fired from a bow, a package dropped from a plane, a rock thrown from a cliff and the bouncing ball on the left are all examples of projectiles Conceptual Physics Chapter 5

14. Projectile Motion The motion of a projectile is a combination of constant velocity in the horizontal direction and constant acceleration in the vertical direction Conceptual Physics Chapter 5

15. Projectile Motion Notice the horizontal velocity vectors remain constant Conceptual Physics Chapter 5

16. Projectile Motion The vertical velocity vectors increase as a result of gravity Conceptual Physics Chapter 5

17. Projectile Motion The velocity (including direction) at any given moment is found by adding the horizontal and vertical components Conceptual Physics Chapter 5

18. Projectile Motion This photograph is taken with the use of a strobe light to capture multiple images of the projectile at equal time intervals. Conceptual Physics Chapter 5

19. Projectile Motion The horizontal spacing between the images of the yellow ball remain constant. The horizontal velocity of a projectile is constant! Conceptual Physics Chapter 5

20. Projectile Motion The vertical spacing between the images of the yellow ball steadily increase. The vertical velocity of a projectile increases due to gravity! Conceptual Physics Chapter 5

21. Projectile Motion The vertical position of the two balls is identical despite the horizontal motion of the yellow ball. The vertical and horizontal motions are independent! Conceptual Physics Chapter 5

22. Question Two identical bullets are set into motion simultaneously. At the instant that the first bullet is fired horizontally from a rifle, the second bullet, held at the same elevation as the rifle, is released and drops to the ground. Which bullet strikes the ground first? Conceptual Physics Chapter 5

23. Projectile Launched at an Angle The vertical motion of the projectile is identical to that of any other body in free fall. The path of the ball if there were no gravity 80 m 45 m 20 m 5 m Conceptual Physics Chapter 5

24. Projectile Launched at an Angle The velocity in the horizontal direction (vx) does not change. Conceptual Physics Chapter 5

25. Projectile Launched at an Angle The velocity in the vertical direction decreases as the object rises. Conceptual Physics Chapter 5

26. Projectile Launched at an Angle The velocity in the vertical direction increases as the object falls. Conceptual Physics Chapter 5

27. Projectile Launched at an Angle Notice the symmetry in the vertical velocity Conceptual Physics Chapter 5

28. Range of a Projectile The horizontal distance the projectile covers is referred to as the range. Range Conceptual Physics Chapter 5

29. v Range of a Projectile Since the horizontal velocity of a projectile remains constant, the range can be found from our definition for velocity. Δx = t Range Conceptual Physics Chapter 5

30. Range of a Projectile Since the horizontal velocity of a projectile remains constant, the range can be found from our definition for velocity. vx Range = vx·t Conceptual Physics Chapter 5

31. Range of a Projectile In order to maximize the range, the projectile should have the greatest horizontal velocity and it should be in the air for the greatest time possible. vx Range = vx·t Conceptual Physics Chapter 5

32. Range of a Projectile For a given launch speed, under what conditions will vx be maximized? When vx is a maximum, t is zero. v vx v Range = vx·t Conceptual Physics Chapter 5

33. Range of a Projectile For a given launch speed, under what conditions will t be maximized? When t is a maximum, vx is zero. v v vx Range = vx·t Conceptual Physics Chapter 5

34. Range of a Projectile The greatest range is produced when the product of vx and t is a maximum. v v 45° vx Range = vx·t Conceptual Physics Chapter 5

35. Range of a Projectile Complementary launch angles result in the same range (neglecting air resistance). Conceptual Physics Chapter 5

36. Range of a Projectile Air resistance reduces the height, range, and time in the air for a projectile launched at any angle. Conceptual Physics Chapter 5