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4. ] Www/boundless.com/physics?campaign_content=book_6 24_chapter_3&campaign_term=Physics&utm_campaign= powerpoint&utm_medium=direct&utm_source=boundless Two-Dimensional Kinematics Motion in Two Dimensions Vectors Projectile Motion Multiple Velocities Free to share, print, make copies and changes. Get yours at www.boundless.com

5. Constant Velocity Constant Acceleration Motion in Two Dimensions Two-Dimensional Kinematics > Motion in Two Dimensions Free to share, print, make copies and changes. Get yours at www.boundless.com www.www/boundless.com/physics?campaign_content=book_624_chapter_3&campaign_term=Physics&utm_campaign=powerpoint&utm_medium =direct&utm_source=boundless

6. Components of a Vector Scalars vs. Vectors Adding and Subtracting Vectors Graphically Adding and Subtracting Vectors Using Components Multiplying Vectors by a Scalar Unit Vectors and Multiplication by a Scalar Position, Displacement, Velocity, and Acceleration as Vectors Vectors Two-Dimensional Kinematics > Vectors Free to share, print, make copies and changes. Get yours at www.boundless.com www.www/boundless.com/physics?campaign_content=book_624_chapter_3&campaign_term=Physics&utm_campaign=powerpoint&utm_medium =direct&utm_source=boundless

7. Basic Equations and Parabolic Path Solving Problems Zero Launch Angle General Launch Angle Key Points: Range, Symmetry, Maximum Height Projectile Motion Two-Dimensional Kinematics > Projectile Motion Free to share, print, make copies and changes. Get yours at www.boundless.com www.www/boundless.com/physics?campaign_content=book_624_chapter_3&campaign_term=Physics&utm_campaign=powerpoint&utm_medium =direct&utm_source=boundless

8. Addition of Velocities Relative Velocity Multiple Velocities Two-Dimensional Kinematics > Multiple Velocities Free to share, print, make copies and changes. Get yours at www.boundless.com www.www/boundless.com/physics?campaign_content=book_624_chapter_3&campaign_term=Physics&utm_campaign=powerpoint&utm_medium =direct&utm_source=boundless

9. Free to share, print, make copies and changes. Get yours at www.boundless.com Appendix

10. Key terms acceleration the rate at which the velocity of a body changes with time axis An imaginary line around which an object spins (an axis of rotation) or is symmetrically arranged (an axis of symmetry). bilateral symmetry the property of being symmetrical about a vertical plane Component A part of a vector. For example, horizontal and vertical components. constant velocity Motion that does not change in speed nor direction. Coordinate axes A set of perpendicular lines which define coordinates relative to an origin. Example: x and y coordinate axes define horizontal and vertical position. coordinates Numbers indicating a position with respect to some axis. Ex: x and y coordinates indicate position relative to x and y axes. displacement The length and direction of a straight line between two objects. gravity Resultant force on Earth's surface, of the attraction by the Earth's masses, and the centrifugal pseudo-force caused by the Earth's rotation. kinematic of or relating to motion or kinematics magnitude A number assigned to a vector indicating its length. Free to share, print, make copies and changes. Get yours at www.boundless.com Two-Dimensional Kinematics

11. magnitude A number assigned to a vector indicating its length. origin The center of a coordinate axis, defined as being the coordinate 0 in all axes. relative Expressed in relation to another item, rather than in complete form. reorientate to orientate anew; to cause to face a different direction scalar A quantity which can be described by a single number, as opposed to a vector which requires a direction and a number. scalar A quantity that has magnitude but not direction; compare vector. symmetrical Exhibiting symmetry; having harmonious or proportionate arrangement of parts; having corresponding parts or relations. trajectory The path of a body as it travels through space. Free to share, print, make copies and changes. Get yours at www.boundless.com Two-Dimensional Kinematics

12. unit vector A vector of magnitude 1. vector A directed quantity, one with both magnitude and direction; the between two points. velocity The rate of change of displacement with respect to change in time. Free to share, print, make copies and changes. Get yours at www.boundless.com Two-Dimensional Kinematics

13. Vector Addition Lesson 1 of 2: Head to Tail Addition Method This video gets viewers started with vector addition and subtraction. The first lesson shows graphical addition while the second video takes a more mathematical approach and shows vector addition by components. Free to share, print, make copies and changes. Get yours at www.boundless.com View on Boundless.com Two-Dimensional Kinematics

14. Graphical Addition of Vectors The head-to-tail method of vector addition requires that you lay out the first vector along a set of coordinate axes. Next, place the tail of the next vector on the head of the first one. Draw a new vector from the origin to the head of the last vector. This new vector is the sum of the original two. Free to share, print, make copies and changes. Get yours at www.boundless.com OpenStax CNX. "OpenStax College, Vector Addition and Subtraction: Graphical Methods. January 24, 2013." CC BY 3.0 http://cnx.org/content/m42127/latest/Figure_03_02_03.jpg View on Boundless.comCC BY 3.0 http://cnx.org/content/m42127/latest/Figure_03_02_03.jpgView on Boundless.com Two-Dimensional Kinematics

15. Vector Addition Lesson 2 of 2: How to Add Vectors by Components This video gets viewers started with vector addition using a mathematical approach and shows vector addition by components. Free to share, print, make copies and changes. Get yours at www.boundless.com View on Boundless.com Two-Dimensional Kinematics

16. Vector with Horizontal and Vertical Components The vector in this image has a magnitude of 10.3 units and a direction of 29.1 degrees above the x-axis. It can be decomposed into a horizontal part and a vertical part as shown. Free to share, print, make copies and changes. Get yours at www.boundless.com OpenStax CNX. "OpenStax College, Vector Addition and Subtraction: Graphical Methods. January 24, 2013." CC BY 3.0 http://cnx.org/content/m42127/latest/Figure_03_02_06a.jpg View on Boundless.comCC BY 3.0 http://cnx.org/content/m42127/latest/Figure_03_02_06a.jpgView on Boundless.com Two-Dimensional Kinematics

17. The difference between Vectors and Scalars, Introduction and Basics This video introduces the difference between scalars and vectors. Ideas about magnitude and direction are introduced and examples of both vectors and scalars are given. Free to share, print, make copies and changes. Get yours at www.boundless.com View on Boundless.com Two-Dimensional Kinematics

18. A Vector An example of a vector. Vectors are usually represented by arrows with their length representing the magnitude and their direction represented by the direction the arrow points. Free to share, print, make copies and changes. Get yours at www.boundless.com Wikimedia. CC BY http://upload.wikimedia.org/wikipedia/commons/thumb/5/5d/Position_vector.svg/220px-Position_vector.svg.png View on Boundless.comCC BYhttp://upload.wikimedia.org/wikipedia/commons/thumb/5/5d/Position_vector.svg/220px-Position_vector.svg.pngView on Boundless.com Two-Dimensional Kinematics

19. Scalar Multiplication (i) Multiplying the vector A by 0.5 halves its length. (ii) Multiplying the vector A by 3 triples its length. (iii) Increasing the mass (scalar) increases the force (vector). Free to share, print, make copies and changes. Get yours at www.boundless.com OpenStax CNX. "Sunil Kumar Singh, Scalar (Dot) Product. January 16, 2015." CC BY 3.0 http://cnx.org/content/m14513/latest/vm2a.gif View on Boundless.comCC BY 3.0http://cnx.org/content/m14513/latest/vm2a.gifView on Boundless.com Two-Dimensional Kinematics

20. Vector Diagram Here is a man walking up a hill. His direction of travel is defined by the angle theta relative to the vertical axis and by the length of the arrow going up the hill. He is also being accelerated downward by gravity. Free to share, print, make copies and changes. Get yours at www.boundless.com Amazon Web Services. "Boundless." CC BY http://s3.amazonaws.com/figures.boundless.com/510a0e5de4b0f11e4bcb01ad/Man_walking_up_a_hill.png View on Boundless.comCC BYhttp://s3.amazonaws.com/figures.boundless.com/510a0e5de4b0f11e4bcb01ad/Man_walking_up_a_hill.pngView on Boundless.com Two-Dimensional Kinematics

21. Vector Addition Addition of velocities is simply the addition of vectors. Free to share, print, make copies and changes. Get yours at www.boundless.com Wikipedia. "Vector Addition and Scaling." CC BY-SA 3.0 http://en.wikipedia.org/wiki/Vector_space View on Boundless.comCC BY-SA 3.0http://en.wikipedia.org/wiki/Vector_spaceView on Boundless.com Two-Dimensional Kinematics

22. Motion with Constant Velocity When an object is moving with constant velocity, it does not change direction nor speed and therefore is represented as a straight line when graphed as distance over time. Free to share, print, make copies and changes. Get yours at www.boundless.com Light and Matter. CC BY http://lightandmatter.com/lmb.pdf View on Boundless.comCC BYhttp://lightandmatter.com/lmb.pdfView on Boundless.com Two-Dimensional Kinematics

23. Launch Angle The launch angle determines the range and maximum height that an object will experience after being launched. This image shows that path of the same object being launched at the same velocity but different angles. Free to share, print, make copies and changes. Get yours at www.boundless.com Wikipedia. "Ideal projectile motion for different angles." CC BY-SA http://en.wikipedia.org/wiki/File:Ideal_projectile_motion_for_different_angles.svg View on Boundless.comCC BY-SAhttp://en.wikipedia.org/wiki/File:Ideal_projectile_motion_for_different_angles.svgView on Boundless.com Two-Dimensional Kinematics

24. Example of multiplying vector by a scalar: gravitational force on an object The gravitational force is a vector whose magnitude is proportional to the scalar quantity known as mass. Since the mass m2 is twice the mass m1 the force of gravity magnitude is doubled as well. Free to share, print, make copies and changes. Get yours at www.boundless.com Marco Mauro public media. "Scalar Vector Product." CC BY-SA 3.0 https://docs.google.com/file/d/0B1yqbp7qd8SKNTdrMHJDSnZPZUE/edit View on Boundless.comCC BY-SA 3.0https://docs.google.com/file/d/0B1yqbp7qd8SKNTdrMHJDSnZPZUE/editView on Boundless.com Two-Dimensional Kinematics

25. Scalar Multiplication (i) Multiplying the vector A by the scalar a = 0.5 yields the vector B which is half as long. (ii) Multiplying the vector A by 3 triples its length. (iii) Doubling the mass (scalar) doubles the force (vector) of gravity. Free to share, print, make copies and changes. Get yours at www.boundless.com OpenStax CNX. "Sunil Kumar Singh, Scalar (Dot) Product. March 12, 2014." CC BY 3.0 http://cnx.org/content/m14513/latest/vm2a.gif View on Boundless.comCC BY 3.0http://cnx.org/content/m14513/latest/vm2a.gifView on Boundless.com Two-Dimensional Kinematics

26. Scalars and Vectors Mr. Andersen explains the differences between scalar and vectors quantities. He also uses a demonstration to show the importance of vectors and vector addition. Free to share, print, make copies and changes. Get yours at www.boundless.com View on Boundless.com Two-Dimensional Kinematics

27. Components of a Vector The original vector, defined relative to a set of axes. The horizontal component stretches from the start of the vector to its furthest x-coordinate. The vertical component stretches from the x-axis to the most vertical point on the vector. Together, the two components and the vector form a right triangle. Free to share, print, make copies and changes. Get yours at www.boundless.com Amazon Web Services. "Boundless." CC BY http://s3.amazonaws.com/figures.boundless.com/5101a2b3e4b04253d8aba44b/vectordecomp.jpg View on Boundless.comCC BYhttp://s3.amazonaws.com/figures.boundless.com/5101a2b3e4b04253d8aba44b/vectordecomp.jpgView on Boundless.com Two-Dimensional Kinematics

28. Projectile Motion Throwing a rock or kicking a ball generally produces a projectile pattern of motion that has both a vertical and a horizontal component. Free to share, print, make copies and changes. Get yours at www.boundless.com OpenStax CNX. "OpenStax College, College Physics. October 19, 2012." CC BY 3.0 http://cnx.org/content/m42042/latest/?collection=col11406/1.7 View on Boundless.comCC BY 3.0http://cnx.org/content/m42042/latest/?collection=col11406/1.7View on Boundless.com Two-Dimensional Kinematics

29. Projectiles at an Angle This video gives a clear and simple explanation of how to solve a problem on Projectiles Launched at an Angle. I try to go step by step through this difficult problem to layout how to solve it in a super clear way. 2D kinematic problems take time to solve, take notes on the order of how I solved it. Best wishes. Tune into my other videos for more help. Peace. Free to share, print, make copies and changes. Get yours at www.boundless.com View on Boundless.com Two-Dimensional Kinematics

30. Range of Trajectory The range of a trajectory is shown in this figure. Free to share, print, make copies and changes. Get yours at www.boundless.com OpenStax CNX. "Sunil Kumar Singh, Features of Projectile Motion. January 25, 2013." CC BY 3.0 http://cnx.org/content/m13847/latest/ View on Boundless.comCC BY 3.0http://cnx.org/content/m13847/latest/View on Boundless.com Two-Dimensional Kinematics

31. How To Solve Any Projectile Motion Problem (The Toolbox Method) Introducing the "Toolbox" method of solving projectile motion problems! Here we use kinematic equations and modify with initial conditions to generate a "toolbox" of equations with which to solve a classic three-part projectile motion problem. Free to share, print, make copies and changes. Get yours at www.boundless.com View on Boundless.com Two-Dimensional Kinematics

32. Diagram for Example 2 When dealing with an object in projectile motion on an incline, we first need to use the given information to reorient the coordinate system in order to have the object launch and fall on the same surface. Free to share, print, make copies and changes. Get yours at www.boundless.com OpenStax CNX. "Sunil Kumar Singh, Projectile Motion on an Incline. February 2, 2013." CC BY 3.0 http://cnx.org/content/m14614/latest/ View on Boundless.comCC BY 3.0http://cnx.org/content/m14614/latest/View on Boundless.com Two-Dimensional Kinematics

33. Diagram for Example 1 Use this figure as a reference to solve example 1. The problem is to make sure the object is able to clear both posts. Free to share, print, make copies and changes. Get yours at www.boundless.com OpenStax CNX. "Sunil Kumar Singh, Features of Projectile Motion. February 2, 2013." CC BY 3.0 http://cnx.org/content/m13847/latest/ View on Boundless.comCC BY 3.0http://cnx.org/content/m13847/latest/View on Boundless.com Two-Dimensional Kinematics

34. Projectile motion Projectile moving following a parabola.Initial launch angle is \alpha, and the velocity is v_0. Free to share, print, make copies and changes. Get yours at www.boundless.com Wikipedia. "Ferde hajitas1." CC BY-SA http://en.wikipedia.org/wiki/File:Ferde_hajitas1.svg View on Boundless.comCC BY-SAhttp://en.wikipedia.org/wiki/File:Ferde_hajitas1.svgView on Boundless.com Two-Dimensional Kinematics

35. Projectile Trajectories The launch angle determines the range and maximum height that an object will experience after being launched.This image shows that path of the same object being launched at the same speed but different angles. Free to share, print, make copies and changes. Get yours at www.boundless.com Wikipedia. "Ideal projectile motion for different angles." CC BY-SA http://en.wikipedia.org/wiki/File:Ideal_projectile_motion_for_different_angles.svg View on Boundless.comCC BY-SAhttp://en.wikipedia.org/wiki/File:Ideal_projectile_motion_for_different_angles.svgView on Boundless.com Two-Dimensional Kinematics

36. Range The range of a projectile motion, as seen in this image, is independent of the forces of gravity. Free to share, print, make copies and changes. Get yours at www.boundless.com OpenStax CNX. "Sunil Kumar Singh, Features of Projectile Motion. January 25, 2013." CC BY 3.0 http://cnx.org/content/m13847/latest/ View on Boundless.comCC BY 3.0http://cnx.org/content/m13847/latest/View on Boundless.com Two-Dimensional Kinematics

37. Free to share, print, make copies and changes. Get yours at www.boundless.com Two-Dimensional Kinematics What must occur in order to have constant velocity? A) The object moves with negligible friction B) All of these answers C) The object must have a constant speed in a constant direction D) The object has zero acceleration

38. Free to share, print, make copies and changes. Get yours at www.boundless.comwww.boundless.com Boundless - LO. "Boundless." CC BY-SA 3.0 http://www.boundless.com/CC BY-SA 3.0http://www.boundless.com/ Two-Dimensional Kinematics What must occur in order to have constant velocity? A) The object moves with negligible friction B) All of these answers C) The object must have a constant speed in a constant direction D) The object has zero acceleration

39. Free to share, print, make copies and changes. Get yours at www.boundless.com Two-Dimensional Kinematics What is the key to analyzing two-dimensional projectile motions? A) Examine the difference in acceleration between the two dimensions B) Examine the two dimensions separately C) Examine the change in distance over time between the two dimensions D) Examine the change in gravity over time

40. Free to share, print, make copies and changes. Get yours at www.boundless.comwww.boundless.com Boundless - LO. "Boundless." CC BY-SA 3.0 http://www.boundless.com/CC BY-SA 3.0http://www.boundless.com/ Two-Dimensional Kinematics What is the key to analyzing two-dimensional projectile motions? A) Examine the difference in acceleration between the two dimensions B) Examine the two dimensions separately C) Examine the change in distance over time between the two dimensions D) Examine the change in gravity over time

41. Free to share, print, make copies and changes. Get yours at www.boundless.com Two-Dimensional Kinematics How do two- and three-dimensional vectors differ from one another? A) The direction is the same, but three-dimensional vectors have three magntiudes B) Two- and three-dimensional are exactly the same C) Two-dimensional vectors include an additional 'z' directional component D) The magnitude is the same, but three-dimensional vectors have three axes

42. Free to share, print, make copies and changes. Get yours at www.boundless.comwww.boundless.com Boundless - LO. "Boundless." CC BY-SA 3.0 http://www.boundless.com/CC BY-SA 3.0http://www.boundless.com/ Two-Dimensional Kinematics How do two- and three-dimensional vectors differ from one another? A) The direction is the same, but three-dimensional vectors have three magntiudes B) Two- and three-dimensional are exactly the same C) Two-dimensional vectors include an additional 'z' directional component D) The magnitude is the same, but three-dimensional vectors have three axes

43. Free to share, print, make copies and changes. Get yours at www.boundless.com Two-Dimensional Kinematics Which of the following should scalars be considered, as opposed to vectors? A) Arrows pointing in a specific direction B) Magnitudes with directions C) Numbers D) Reference points on an x-y plane

44. Free to share, print, make copies and changes. Get yours at www.boundless.comwww.boundless.com Boundless - LO. "Boundless." CC BY-SA 3.0 http://www.boundless.com/CC BY-SA 3.0http://www.boundless.com/ Two-Dimensional Kinematics Which of the following should scalars be considered, as opposed to vectors? A) Arrows pointing in a specific direction B) Magnitudes with directions C) Numbers D) Reference points on an x-y plane

45. Free to share, print, make copies and changes. Get yours at www.boundless.com Two-Dimensional Kinematics What is another name for the graphical method of vector addition? A) Coordinate axes method B) Head-to-tail method C) Commutative method D) Origin of the chain method

46. Free to share, print, make copies and changes. Get yours at www.boundless.comwww.boundless.com Boundless - LO. "Boundless." CC BY-SA 3.0 http://www.boundless.com/CC BY-SA 3.0http://www.boundless.com/ Two-Dimensional Kinematics What is another name for the graphical method of vector addition? A) Coordinate axes method B) Head-to-tail method C) Commutative method D) Origin of the chain method

47. Free to share, print, make copies and changes. Get yours at www.boundless.com Two-Dimensional Kinematics How do you subtract vectors by components? A) Subtract first horizontal from first vertical and second horizontal from second vertical B) Subtract first vertical from first horizontal and second vertical from second horizontal C) It's not possible to subtract vectors, only to add vectors D) Subtract horizontal from each other and subtract vertical from each other

48. Free to share, print, make copies and changes. Get yours at www.boundless.comwww.boundless.com Boundless - LO. "Boundless." CC BY-SA 3.0 http://www.boundless.com/CC BY-SA 3.0http://www.boundless.com/ Two-Dimensional Kinematics How do you subtract vectors by components? A) Subtract first horizontal from first vertical and second horizontal from second vertical B) Subtract first vertical from first horizontal and second vertical from second horizontal C) It's not possible to subtract vectors, only to add vectors D) Subtract horizontal from each other and subtract vertical from each other

49. Free to share, print, make copies and changes. Get yours at www.boundless.com Two-Dimensional Kinematics What is the velocity given the two scalars of 10 seconds and 50 meters? A) 5 m/s B) 0.2 m/s C) 500 ms D) 5 m/s2

50. Free to share, print, make copies and changes. Get yours at www.boundless.comwww.boundless.com Boundless - LO. "Boundless." CC BY-SA 3.0 http://www.boundless.com/CC BY-SA 3.0http://www.boundless.com/ Two-Dimensional Kinematics What is the velocity given the two scalars of 10 seconds and 50 meters? A) 5 m/s B) 0.2 m/s C) 500 ms D) 5 m/s2

51. Free to share, print, make copies and changes. Get yours at www.boundless.com Two-Dimensional Kinematics What do the unit vectors in Cartesian coordinates describe? A) An object's magnitude B) An angle between two vectors C) A constant scalar D) A circle with a radius of one

52. Free to share, print, make copies and changes. Get yours at www.boundless.comwww.boundless.com Boundless - LO. "Boundless." CC BY-SA 3.0 http://www.boundless.com/CC BY-SA 3.0http://www.boundless.com/ Two-Dimensional Kinematics What do the unit vectors in Cartesian coordinates describe? A) An object's magnitude B) An angle between two vectors C) A constant scalar D) A circle with a radius of one

53. Free to share, print, make copies and changes. Get yours at www.boundless.com Two-Dimensional Kinematics Which of the following is an example of velocity? A) 100 m/s B) 100 m/s2 C) 100 m D) 100 s

54. Free to share, print, make copies and changes. Get yours at www.boundless.comwww.boundless.com Boundless - LO. "Boundless." CC BY-SA 3.0 http://www.boundless.com/CC BY-SA 3.0http://www.boundless.com/ Two-Dimensional Kinematics Which of the following is an example of velocity? A) 100 m/s B) 100 m/s2 C) 100 m D) 100 s

55. Free to share, print, make copies and changes. Get yours at www.boundless.com Two-Dimensional Kinematics In projectile motion, what is the acceleration in the vertical direction? A) -10 m/s2 B) 10 m/s2 C) 0 m/s2 D) Equivalent to the horizontal direction

56. Free to share, print, make copies and changes. Get yours at www.boundless.comwww.boundless.com Boundless - LO. "Boundless." CC BY-SA 3.0 http://www.boundless.com/CC BY-SA 3.0http://www.boundless.com/ Two-Dimensional Kinematics In projectile motion, what is the acceleration in the vertical direction? A) -10 m/s2 B) 10 m/s2 C) 0 m/s2 D) Equivalent to the horizontal direction

57. Free to share, print, make copies and changes. Get yours at www.boundless.com Two-Dimensional Kinematics Which of the following components are key to projectile motion: (1) force, (2) velocity, (3) displacement, (4) range? A) (1), (2), (3) B) (1), (3), (4) C) (2), (3), (4) D) (2), (3)

58. Free to share, print, make copies and changes. Get yours at www.boundless.comwww.boundless.com Boundless - LO. "Boundless." CC BY-SA 3.0 http://www.boundless.com/CC BY-SA 3.0http://www.boundless.com/ Two-Dimensional Kinematics Which of the following components are key to projectile motion: (1) force, (2) velocity, (3) displacement, (4) range? A) (1), (2), (3) B) (1), (3), (4) C) (2), (3), (4) D) (2), (3)

59. Free to share, print, make copies and changes. Get yours at www.boundless.com Two-Dimensional Kinematics Which of the following does the angle dictate in projectile motion? A) Range B) Height C) All of these answers D) Time of flight

60. Free to share, print, make copies and changes. Get yours at www.boundless.comwww.boundless.com Boundless - LO. "Boundless." CC BY-SA 3.0 http://www.boundless.com/CC BY-SA 3.0http://www.boundless.com/ Two-Dimensional Kinematics Which of the following does the angle dictate in projectile motion? A) Range B) Height C) All of these answers D) Time of flight

61. Free to share, print, make copies and changes. Get yours at www.boundless.com Two-Dimensional Kinematics If a monkey throws a banana at an angle of 45° at 10 m/s, what is the time of flight of the banana? A) 3.6 s B) 1.7 s C) 17 s D) 7.24 s

62. Free to share, print, make copies and changes. Get yours at www.boundless.comwww.boundless.com Boundless - LO. "Boundless." CC BY-SA 3.0 http://www.boundless.com/CC BY-SA 3.0http://www.boundless.com/ Two-Dimensional Kinematics If a monkey throws a banana at an angle of 45° at 10 m/s, what is the time of flight of the banana? A) 3.6 s B) 1.7 s C) 17 s D) 7.24 s

63. Free to share, print, make copies and changes. Get yours at www.boundless.com Two-Dimensional Kinematics What is the name of the path an object follows? A) Projectile motion B) Bilateral symmetry C) Trajectory D) Gravity

64. Free to share, print, make copies and changes. Get yours at www.boundless.comwww.boundless.com Boundless - LO. "Boundless." CC BY-SA 3.0 http://www.boundless.com/CC BY-SA 3.0http://www.boundless.com/ Two-Dimensional Kinematics What is the name of the path an object follows? A) Projectile motion B) Bilateral symmetry C) Trajectory D) Gravity

65. Attribution OpenStax CNX. "OpenStax College, Vector Addition and Subtraction: Graphical Methods. September 17, 2013." CC BY 3.0 http://cnx.org/content/m42127/latest/CC BY 3.0 http://cnx.org/content/m42127/latest/ Wiktionary. "origin." CC BY-SA 3.0 http://en.wiktionary.org/wiki/originCC BY-SA 3.0http://en.wiktionary.org/wiki/origin Boundless Learning. "Boundless." CC BY-SA 3.0 http://www.boundless.com//physics/definition/coordinate-axesCC BY-SA 3.0http://www.boundless.com//physics/definition/coordinate-axes Boundless Learning. "Boundless." CC BY-SA 3.0 http://www.boundless.com//physics/definition/componentCC BY-SA 3.0http://www.boundless.com//physics/definition/component OpenStax CNX. "OpenStax College, Vector Addition and Subtraction: Graphical Methods. September 17, 2013." CC BY 3.0 http://cnx.org/content/m42127/latest/CC BY 3.0 http://cnx.org/content/m42127/latest/ Wikipedia. "Euclidean vector." CC BY-SA 3.0 http://en.wikipedia.org/wiki/Euclidean_vectorCC BY-SA 3.0http://en.wikipedia.org/wiki/Euclidean_vector Wikipedia. "Scalar (physics)." CC BY-SA 3.0 http://en.wikipedia.org/wiki/Scalar_(physics)CC BY-SA 3.0http://en.wikipedia.org/wiki/Scalar_(physics) Boundless Learning. "Boundless." CC BY-SA 3.0 http://www.boundless.com//physics/definition/coordinate-axesCC BY-SA 3.0http://www.boundless.com//physics/definition/coordinate-axes OpenStax CNX. "Sunil Kumar Singh, Scalar (Dot) Product. September 17, 2013." CC BY 3.0 http://cnx.org/content/m14513/latest/CC BY 3.0 http://cnx.org/content/m14513/latest/ Wikipedia. "Scalar (physics)." CC BY-SA 3.0 http://en.wikipedia.org/wiki/Scalar_(physics)CC BY-SA 3.0http://en.wikipedia.org/wiki/Scalar_(physics) Wikipedia. "Unit vector." CC BY-SA 3.0 http://en.wikipedia.org/wiki/Unit_vectorCC BY-SA 3.0http://en.wikipedia.org/wiki/Unit_vector Wiktionary. "unit vector." CC BY-SA 3.0 http://en.wiktionary.org/wiki/unit+vectorCC BY-SA 3.0http://en.wiktionary.org/wiki/unit+vector Wiktionary. "scalar." CC BY-SA 3.0 http://en.wiktionary.org/wiki/scalarCC BY-SA 3.0http://en.wiktionary.org/wiki/scalar Wikipedia. "Displacement (vector)." CC BY-SA 3.0 http://en.wikipedia.org/wiki/Displacement_(vector)CC BY-SA 3.0http://en.wikipedia.org/wiki/Displacement_(vector) Wiktionary. "acceleration." CC BY-SA 3.0 http://en.wiktionary.org/wiki/accelerationCC BY-SA 3.0http://en.wiktionary.org/wiki/acceleration Wiktionary. "velocity." CC BY-SA 3.0 http://en.wiktionary.org/wiki/velocityCC BY-SA 3.0http://en.wiktionary.org/wiki/velocity Wiktionary. "displacement." CC BY-SA 3.0 http://en.wiktionary.org/wiki/displacementCC BY-SA 3.0http://en.wiktionary.org/wiki/displacement Free to share, print, make copies and changes. Get yours at www.boundless.com Two-Dimensional Kinematics

66. Wikipedia. "Relative velocity." CC BY-SA 3.0 http://en.wikipedia.org/wiki/Relative_velocityCC BY-SA 3.0http://en.wikipedia.org/wiki/Relative_velocity Wikipedia. "Velocity-addition formula." CC BY-SA 3.0 http://en.wikipedia.org/wiki/Velocity-addition_formulaCC BY-SA 3.0http://en.wikipedia.org/wiki/Velocity-addition_formula OpenStax CNX. "Sunil Kumar Singh, Relative Velocity in Two Dimensions. September 17, 2013." CC BY 3.0 http://cnx.org/content/m14030/latest/CC BY 3.0 http://cnx.org/content/m14030/latest/ Wiktionary. "relative." CC BY-SA 3.0 http://en.wiktionary.org/wiki/relativeCC BY-SA 3.0http://en.wiktionary.org/wiki/relative OpenStax CNX. "OpenStax College, Addition of Velocities. September 17, 2013." CC BY 3.0 http://cnx.org/content/m42045/latest/CC BY 3.0 http://cnx.org/content/m42045/latest/ Wikipedia. "Velocity-addition formula." CC BY-SA 3.0 http://en.wikipedia.org/wiki/Velocity-addition_formulaCC BY-SA 3.0http://en.wikipedia.org/wiki/Velocity-addition_formula Wiktionary. "relative." CC BY-SA 3.0 http://en.wiktionary.org/wiki/relativeCC BY-SA 3.0http://en.wiktionary.org/wiki/relative Wikipedia. "Velocity." CC BY-SA 3.0 http://en.wikipedia.org/wiki/VelocityCC BY-SA 3.0http://en.wikipedia.org/wiki/Velocity Boundless Learning. "Boundless." CC BY-SA 3.0 http://www.boundless.com//physics/definition/constant-velocityCC BY-SA 3.0http://www.boundless.com//physics/definition/constant-velocity Light and Matter. CC BY http://lightandmatter.com/lmb.pdfCC BYhttp://lightandmatter.com/lmb.pdf Wikipedia. "Trajectory of a projectile." CC BY-SA 3.0 http://en.wikipedia.org/wiki/Trajectory_of_a_projectileCC BY-SA 3.0http://en.wikipedia.org/wiki/Trajectory_of_a_projectile Wikipedia. "Trajectory." CC BY-SA 3.0 http://en.wikipedia.org/wiki/TrajectoryCC BY-SA 3.0http://en.wikipedia.org/wiki/Trajectory OpenStax CNX. "Sunil Kumar Singh, Features of Projectile Motion. September 17, 2013." CC BY 3.0 http://cnx.org/content/m13847/latest/CC BY 3.0 http://cnx.org/content/m13847/latest/ Wiktionary. "trajectory." CC BY-SA 3.0 http://en.wiktionary.org/wiki/trajectoryCC BY-SA 3.0http://en.wiktionary.org/wiki/trajectory OpenStax CNX. "Sunil Kumar Singh, Scalar (Dot) Product. September 17, 2013." CC BY 3.0 http://cnx.org/content/m14513/latest/CC BY 3.0 http://cnx.org/content/m14513/latest/ Wiktionary. "magnitude." CC BY-SA 3.0 http://en.wiktionary.org/wiki/magnitudeCC BY-SA 3.0http://en.wiktionary.org/wiki/magnitude Wiktionary. "scalar." CC BY-SA 3.0 http://en.wiktionary.org/wiki/scalarCC BY-SA 3.0http://en.wiktionary.org/wiki/scalar Wiktionary. "vector." CC BY-SA 3.0 http://en.wiktionary.org/wiki/vectorCC BY-SA 3.0http://en.wiktionary.org/wiki/vector OpenStax CNX. "Sunil Kumar Singh, Components of a Vector. September 17, 2013." CC BY 3.0 http://cnx.org/content/m14519/latest/CC BY 3.0 http://cnx.org/content/m14519/latest/ Free to share, print, make copies and changes. Get yours at www.boundless.com Two-Dimensional Kinematics

67. Wikipedia. "Euclidean vector." CC BY-SA 3.0 http://en.wikipedia.org/wiki/Euclidean_vectorCC BY-SA 3.0http://en.wikipedia.org/wiki/Euclidean_vector Wiktionary. "axis." CC BY-SA 3.0 http://en.wiktionary.org/wiki/axisCC BY-SA 3.0http://en.wiktionary.org/wiki/axis Wikipedia. "coordinates." CC BY-SA 3.0 http://en.wikipedia.org/wiki/coordinatesCC BY-SA 3.0http://en.wikipedia.org/wiki/coordinates Wiktionary. "magnitude." CC BY-SA 3.0 http://en.wiktionary.org/wiki/magnitudeCC BY-SA 3.0http://en.wiktionary.org/wiki/magnitude OpenStax CNX. "OpenStax College, College Physics. September 17, 2013." CC BY 3.0 http://cnx.org/content/m42042/latest/?collection=col11406/1.7CC BY 3.0 http://cnx.org/content/m42042/latest/?collection=col11406/1.7 Wikipedia. "Acceleration." CC BY-SA 3.0 http://en.wikipedia.org/wiki/AccelerationCC BY-SA 3.0http://en.wikipedia.org/wiki/Acceleration Wiktionary. "kinematic." CC BY-SA 3.0 http://en.wiktionary.org/wiki/kinematicCC BY-SA 3.0http://en.wiktionary.org/wiki/kinematic Wiktionary. "trajectory." CC BY-SA 3.0 http://en.wiktionary.org/wiki/trajectoryCC BY-SA 3.0http://en.wiktionary.org/wiki/trajectory Wiktionary. "symmetrical." CC BY-SA 3.0 http://en.wiktionary.org/wiki/symmetricalCC BY-SA 3.0http://en.wiktionary.org/wiki/symmetrical OpenStax CNX. "Sunil Kumar Singh, Features of Projectile Motion. September 18, 2013." CC BY 3.0 http://cnx.org/content/m13847/latest/CC BY 3.0 http://cnx.org/content/m13847/latest/ Wikipedia. "Projectile motion." CC BY-SA 3.0 http://en.wikipedia.org/wiki/Projectile_motionCC BY-SA 3.0http://en.wikipedia.org/wiki/Projectile_motion OpenStax CNX. "Sunil Kumar Singh, Features of Projectile Motion. September 18, 2013." CC BY 3.0 http://cnx.org/content/m13847/latest/CC BY 3.0 http://cnx.org/content/m13847/latest/ OpenStax CNX. "Sunil Kumar Singh, Projectile Motion on an Incline. September 18, 2013." CC BY 3.0 http://cnx.org/content/m14614/latest/CC BY 3.0 http://cnx.org/content/m14614/latest/ Wiktionary. "reorientate." CC BY-SA 3.0 http://en.wiktionary.org/wiki/reorientateCC BY-SA 3.0http://en.wiktionary.org/wiki/reorientate OpenStax CNX. "Sunil Kumar Singh, Features of Projectile Motion. September 18, 2013." CC BY 3.0 http://cnx.org/content/m13847/latest/CC BY 3.0 http://cnx.org/content/m13847/latest/ Wiktionary. "trajectory." CC BY-SA 3.0 http://en.wiktionary.org/wiki/trajectoryCC BY-SA 3.0http://en.wiktionary.org/wiki/trajectory Wikipedia. "Trajectory of a projectile." CC BY-SA 3.0 http://en.wikipedia.org/wiki/Trajectory_of_a_projectileCC BY-SA 3.0http://en.wikipedia.org/wiki/Trajectory_of_a_projectile Wikipedia. "Trajectory." CC BY-SA 3.0 http://en.wikipedia.org/wiki/TrajectoryCC BY-SA 3.0http://en.wikipedia.org/wiki/Trajectory Wikipedia. "Projectile motion." CC BY-SA 3.0 http://en.wikipedia.org/wiki/Projectile_motionCC BY-SA 3.0http://en.wikipedia.org/wiki/Projectile_motion Free to share, print, make copies and changes. Get yours at www.boundless.com Two-Dimensional Kinematics

68. OpenStax CNX. "Sunil Kumar Singh, Features of Projectile Motion. September 18, 2013." CC BY 3.0 http://cnx.org/content/m13847/latest/CC BY 3.0 http://cnx.org/content/m13847/latest/ Wiktionary. "gravity." CC BY-SA 3.0 http://en.wiktionary.org/wiki/gravityCC BY-SA 3.0http://en.wiktionary.org/wiki/gravity Wiktionary. "trajectory." CC BY-SA 3.0 http://en.wiktionary.org/wiki/trajectoryCC BY-SA 3.0http://en.wiktionary.org/wiki/trajectory Wiktionary. "bilateral symmetry." CC BY-SA 3.0 http://en.wiktionary.org/wiki/bilateral+symmetryCC BY-SA 3.0http://en.wiktionary.org/wiki/bilateral+symmetry Free to share, print, make copies and changes. Get yours at www.boundless.com Two-Dimensional Kinematics