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### Transcript of Chapter 3. vectors projectiles

• 1. Two-Dimensional Motion and Vectors Chapter 3
• 2. Introduction to Vectors A scalar is a quantity that can be completely specified by its magnitude A vector is a physical quantity that has both magnitude and direction. Some examples of vector quantities are velocity, acceleration, displacement and forces. Vectors can be added graphically, but when adding vectors you must be sure that they have the same units and that the vectors describe similar quantities. The answer found by adding vectors is called the resultant.
• 3. Vector operations The magnitude and direction of the resultant of two perpendicular vectors can be calculated using the Pythagorean Theorem and the tangent function. Magnitude of vector Pythagorean Theorem Direction of vector Tangent function
• 4. Basic Vector Operations Both a magnitude and a direction must be specified for a vector quantity, in contrast to a scalar quantity which can be quantified with just a number. Any number of vector quantities of the same type (i.e., same units) can be combined by basic vector operations.
• 5. Addition of 2 Vectors
• 6. Addition of 3 Vectors
• 7. Set # 9 P/3 A football player runs 15 m down the field, and then turns to the left at an angle of 15 from his original direction and running an additional 10 m before getting tackled Find the magnitude and direction 15 m 10m 15 Bx By
• 8. P/5 Set # 9 A person walks the path shown below, whats is the person resultant displacement measured from the starting person 60 30 100 m 300 m 150 m 200 m ? Ax = ______ Ay = ______ Bx = ______ By = ______ Cx = ______ Cy = ______ Dx = ______ Dy = ______ x = ______ y = ______ Resultant Vector
• 9. Example 4: A plane flies from city A to city B. City B is 1,540 km west and 1,160 km south of city A. What is the total displacement and direction of the plane? a) 1,930 km, 43 south of west b) 1,850 km, 43 south of west c) 1,850 km, 37 south of west d) 1,930 km, 37 south of west
• 10. A plane flies from city A to city B. City B is 1,540 km west and 1,160 km south of city A. What is the total displacement and direction of the plane? A 1,540 km 1,160 km B
• 11. Example # 5 During a rodeo, a clown runs 8 m north, turns 35 east of north and runs 3.5 m. Then after awaiting for the bull to come near, the clown turns due east and runs 5m to exit the arena. Find the clowns displacement 35 8 m 3.5m 5 m Ax = _____ Ay = _____ Bx = _____ By = _____ Cx = _____ Cy = _____ x = _____ y = _____ Resultant Vector
• 12. Example 6: A duck waddles 2.5 m east and 6 m north. What is the magnitude and direction of the ducks displacement with respect to its original position? a) 3.5 m at 19 north of east b) 6.3 m at 67 north of east c) 6.5 m at 67 north of east d) 6.5 m at 72 north of east
• 13. Physics Set # 10 Oct/2/2007 Student Name: ____________________________________ Class Period: _______ P/1 A person walks the path shown below: a) Find the persons resultant displacement measured from the starting point b) Determine the direction Answers: a)__________ b) ________ P/2 A person walks the path shown below: a) Find the persons resultant displacement measured from the starting point b) Determine the direction Answers: a)_________ b) _________ 150 m 300 m 150 m 30 60 120 m 20 500 m 250 m 125 m 160 m 25 15
• 14. Physics Set # 11 Oct/3/2007 Student Name: ____________________________________ Class Period: _______ P/1 Mr. C designed play 2244 in football that will send a receiver down the field as explained in the following diagram. a) Find the displacement of this receiver b) Find the direction Answers: a) _________ b) _________ P/2 Mr. C designed play 4877 in football that will send a receiver down the field as explained in the following diagram. a) Find the displacement of this receiver b) Find the direction Answers: a) _________ b) ________ 50 7 yds 6 yds 5 yds 30 14 yds 10 yds 6 yds 20 4 yds 12 yds
• 15. Physics Set # 12 Oct/4/2007 Student Name: ____________________________________ Class Period: _______ P/1 Mr. C designed play 485 in football that will send a receiver down the field as explained in the following diagram. a) Find the displacement of this receiver b) Find the direction Answers: a) _________ b) _________ P/2 Mr. C designed play 4877 in football that will send a receiver down the field as explained in the following diagram. a) Find the displacement of this receiver b) Find the direction Answers: a) _________ b) _________ 60 6 yds 4 yds 3 yds 40 16 yds 15 yds 7 yds 40 5yds 11 yds 20 8 yds 75
• 16. Physics Set # 13 Oct/4/2007 Student Name: ____________________________________ Class Period: _______ P/1 Mr. C designed play 775 in football that will send a receiver down the field as explained in the following diagram. a) Find the displacement of this receiver b) Find the direction Answers: a) _________ b) _________ P/2 Mr. C designed play 4877 in football that will send a receiver down the field as explained in the following diagram. a) Find the displacement of this receiver b) Find the direction Answers: a) _________ b) _________ 60 6 yds 4 yds 40 12 yds 12 yds 7 yds 40 5yds 8 yds 18 yds 65
• 17. P/3 A person walks the path shown below: a) Find the persons resultant displacement measured from the starting point b) Determine the direction Answers: a)__________ b) ________ P/4 A person walks the path shown below: a) Find the persons resultant displacement measured from the starting point b) Determine the direction Answers: a)_________ b) _________ 180 m 250 m 60 m 30 60 50 m 20 500m 250 m 125 m 160 m 25 15 20
• 18. Vectors The study of vectors allows for breaking a single vector into components: the vertical component the horizontal component. By breaking a single vector into two components, or resolving it into its components, an objects motion can sometimes be described more conveniently in terms of directions, such as north to south, or up and down. vy vx vi
• 19. Essay: Wernher von Braun 2 pages/ 12 font Chunk Paragraph: topic sentence + 2 concrete details +4 commentaries + concluding sentence The early childhood Family His achievements in Germany His involvement in the Nazi Party How did he ended up in U.S.A.? His achievements in U.S.A.
• 20. Projectile Motion
• 21. Projectile Motion A projectile is any object upon which the only force acting is gravity. Projectiles travel with a parabolic trajectory due to the influence of gravity, There are no horizontal forces acting upon projectiles and thus no horizontal acceleration, The horizontal velocity of a projectile is constant (never changing in value), There is a vertical acceleration caused by gravity; its value is -9.81 m/s, down. The vertical velocity of a projectile changes by 9.81 m/s each second. The horizontal motion of a projectile is independent of its vertical motion.
• 22. Projectile Motion A projectile is an