1. Vectors and Two-Dimensional Motion

2. 3-01 Vectors and Their Properties 3-02 Components of a Vector 3-04 Motion in Two Dimensions Vectors & Two-Dimensional Motion 3-05 Relative Velocity Topics Vectors and Two-Dimensional Motion (Phy 2053): vittitoe

3. ScalarsVectors Distance Time Mass Work Energy Speed Displacement Velocity Acceleration Force Momentum Torque Magnitude Only Magnitude and Direction Vectors ad Their Properties Vectors and Two-Dimensional Motion (Phy 2053): vittitoe

4. Vectors have magnitude and direction, but no place Vectors ad Their Properties Vectors and Two-Dimensional Motion (Phy 2053): vittitoe

5. Two vectors are equal if they have the same magnitude and the same direction Vectors ad Their Properties Vectors and Two-Dimensional Motion (Phy 2053): vittitoe

6. Scaling Vectors Vectors ad Their Properties s Vectors and Two-Dimensional Motion (Phy 2053): vittitoe

7. Scaling a Displacement Vector Vectors ad Their Properties Vectors and Two-Dimensional Motion (Phy 2053): vittitoe

8. Scaling a Change in Velocity Vector Vectors ad Their Properties Vectors and Two-Dimensional Motion (Phy 2053): vittitoe

9. Vector Addition (Graphical) Vectors ad Their Properties Vectors and Two-Dimensional Motion (Phy 2053): vittitoe

10. Vector Subtraction (Graphical) (A  B) Vectors ad Their Properties Vectors and Two-Dimensional Motion (Phy 2053): vittitoe

11. x y Components of a Vector Vectors and Two-Dimensional Motion (Phy 2053): vittitoe

12. x y Vector Components Components of a Vector Vectors and Two-Dimensional Motion (Phy 2053): vittitoe

13. x y Vector Components Components of a Vector Vectors and Two-Dimensional Motion (Phy 2053): vittitoe

14. A B R AxAx BxBx RxRx AyAy ByBy RyRy x y Components of a Vector Vectors and Two-Dimensional Motion (Phy 2053): vittitoe

15. A B R AxAx BxBx RxRx AyAy ByBy RyRy x y Components of a Vector Vectors and Two-Dimensional Motion (Phy 2053): vittitoe

16. F2F2 22 F3F3 33 F4F4 44 F1F1 11 Components of a Vector Adding Vectors Vectors and Two-Dimensional Motion (Phy 2053): vittitoe

17. F1F1 F2F2 F3F3 F4F4 11 22 33 44 F 1 = 50 N  1 = 30 o F 2 = 100 N  2 = 135 o F 3 = 30 N  3 = 250 o F 4 = 40 N  4 = 300 o 43.325.0  70.7 70.7  10.3  28.2 20.0  34.6  17.7 32.9 Components of a Vector Vectors and Two-Dimensional Motion (Phy 2053): vittitoe

18. F R = 37.4 N RR   17.7 32.9 Components of a Vector Vectors and Two-Dimensional Motion (Phy 2053): vittitoe

19. F1F1 F2F2 F3F3 F4F4 11 22 33 44 F 1 = 90 N  1 = 45 o F 2 = 80 N  2 = 150 o F 3 =50 N  3 = 220 o F 4 = 70 N  4 = 340 o Components of a Vector Add the following vectors Vectors and Two-Dimensional Motion (Phy 2053): vittitoe

20. Motion in Two Dimensions Vectors and Two-Dimensional Motion (Phy 2053): vittitoe

21. a y =  g a x = 0 Motion in Two Dimensions Vectors and Two-Dimensional Motion (Phy 2053): vittitoe

22. Ignoring air resistance, the horizontal component of a projectile's acceleration A) is zero. B) remains a non-zero constant. C) continuously increases. D) continuously decreases. Vectors and Two-Dimensional Motion (Phy 2053): vittitoe Motion in Two Dimensions

23. If an object is launched at an initial angle of θ with the horizontal, the analysis is similar except that the initial velocity has a vertical component.  Motion in Two Dimensions Vectors and Two-Dimensional Motion (Phy 2053): vittitoe

24. Ignoring air resistance, the horizontal component of a projectile's velocity A) is zero. B) remains constant. C) continuously increases. D) continuously decreases. Vectors and Two-Dimensional Motion (Phy 2053): vittitoe Motion in Two Dimensions

25.  vovo x yAt t = 0 Eq 2 Constant acceleration Eq 1 Constant velocity Motion in Two Dimensions Vectors and Two-Dimensional Motion (Phy 2053): vittitoe

26. A ball is thrown with a velocity of 20 m/s at an angle of 60° above the horizontal. What is the horizontal component of its instantaneous velocity at the exact top of its trajectory? A) 10 m/s B) 20 m/s C) 5.0 m/s D) zero Vectors and Two-Dimensional Motion (Phy 2053): vittitoe Motion in Two Dimensions

27.  vovo x y Sub Eq 1 Eq 3 Constant velocity Motion in Two Dimensions Vectors and Two-Dimensional Motion (Phy 2053): vittitoe Horizontal Position

28. EOC Problem 03-04 If V x = 6.80 units and V y =  7.40 units, a) determine the magnitude of V. b) determine the direction of V VxVx V VyVy  Vectors and Two-Dimensional Motion (Phy 2053): vittitoe

29.  vovo x y Eq 4 Constant acceleration Motion in Two Dimensions Vectors and Two-Dimensional Motion (Phy 2053): vittitoe Vertical Position

30. A soccer ball is kicked with a velocity of 25 m/s at an angle of 45° above the horizontal. What is the vertical component of its acceleration as it travels along its trajectory? A) 9.80 m/s 2 downward B) (9.80 m/s 2 ) × sin (45°) downward C) (9.80 m/s 2 ) × sin (45°) upward D) (9.80 m/s 2 ) upward Vectors and Two-Dimensional Motion (Phy 2053): vittitoe Motion in Two Dimensions

31. A diver running 1.8 m/s dives out horizontally from the edge of a vertical cliff and 3.0 s later reaches the water below. a) How high was the cliff? EOC Problem 03-18 h d v b) How far from its base did the diver hit the water? Vectors and Two-Dimensional Motion (Phy 2053): vittitoe

32.  vovo h x y Sub into Eq 4 Eq 5 Solve Eq 3 for t Motion in Two Dimensions Vertical Position as a Function of Horizontal Displacement Vectors and Two-Dimensional Motion (Phy 2053): vittitoe

33.  vovo h x y At the maximum height (v y = 0) Sub into Eq 4 Eq 7 Eq 6 Motion in Two Dimensions Maximum Height Vectors and Two-Dimensional Motion (Phy 2053): vittitoe

34. When a football in a field goal attempt reaches its maximum height, how does its speed compare to its initial speed? A) It is zero. B) It is equal to its initial speed. C) It is greater than its initial speed. D) It is less than its initial speed. Vectors and Two-Dimensional Motion (Phy 2053): vittitoe Motion in Two Dimensions

35. EOC Problem 03-22 A football is kicked at ground level with a speed of 18.0 m/s at an angle of 35.0º to the horizontal. How much later does it hit the ground? Vectors and Two-Dimensional Motion (Phy 2053): vittitoe

36.  vovo R h x y Eq 8 Motion in Two Dimensions Range Vectors and Two-Dimensional Motion (Phy 2053): vittitoe

37. At what angle should a water-gun be aimed in order for the water to land with the greatest horizontal range? A) 0° B) 30° C) 45° D) 60° Vectors and Two-Dimensional Motion (Phy 2053): vittitoe Motion in Two Dimensions

38. A projectile is fired with an initial speed of 65.2 m/s at an angle of 34.5º above the horizontal on a long flat firing range. Determine (a) the maximum height reached by the projectile. EOC Problem 03-30 (b) the total time in the air (c) the total horizontal distance covered (that is, the range). Vectors and Two-Dimensional Motion (Phy 2053): vittitoe

39. Eq 1 Horizontal Velocity Eq 2 Vertical Velocity Eq 3 Horizontal Displacement Eq 4 Vertical Displacement Equations Vectors and Two-Dimensional Motion (Phy 2053): vittitoe

40. Eq 5 Vertical Position Eq 7 Maximum Height Eq 8 RangeEq 6 Time to the Top Equations Vectors and Two-Dimensional Motion (Phy 2053): vittitoe

41. vwvw d vwvw vSvS vBvB vBvB L Relative Velocity Vectors and Two-Dimensional Motion (Phy 2053): vittitoe

42. vSvS L vBvB vwvw  Time required to go directly across. Relative Velocity Vectors and Two-Dimensional Motion (Phy 2053): vittitoe

43. You are trying to cross a river that flows due south with a strong current. You start out in your motorboat on the east bank desiring to reach the west bank directly west from your starting point. You should head your motorboat A) due west. B) due north. C) in a southwesterly direction. D) in a northwesterly direction. Vectors and Two-Dimensional Motion (Phy 2053): vittitoe Motion in Two Dimensions