2D-Motion

1. 2D-Motion Introduction

2. Chapter 3. Reading Quizzes

3. What is a vector? • A quantity having both size and direction • The rate of change of velocity • A number defined by an angle and a magnitude • The difference between initial and final displacement • None of the above

4. What is a vector? • A quantity having both size and direction • The rate of change of velocity • A number defined by an angle and a magnitude • The difference between initial and final displacement • None of the above

5. What is the name of the quantity represented as ? ^ • Eye-hat • Invariant magnitude • Integral of motion • Unit vector in x-direction • Length of the horizontal axis

6. What is the name of the quantity represented as ? ^ • Eye-hat • Invariant magnitude • Integral of motion • Unit vector in x-direction • Length of the horizontal axis

7. This chapter shows how vectors can be added using • graphical addition. • algebraic addition. • numerical addition. • both A and B. • both A and C.

8. This chapter shows how vectors can be added using • graphical addition. • algebraic addition. • numerical addition. • both A and B. • both A and C.

9. To decompose a vector means • to break it into several smaller vectors. • to break it apart into scalars. • to break it into pieces parallel to the axes. • to place it at the origin. • This topic was not discussed in Chapter 3.

10. To decompose a vector means • to break it into several smaller vectors. • to break it apart into scalars. • to break it into pieces parallel to the axes. • to place it at the origin. • This topic was not discussed in Chapter 3.

11. Chapter 3. Concept Questions

12. Which figure shows ?

13. Which figure shows ?

14. Which figure shows 2 − ?

15. Which figure shows 2 − ?

16. What are the x- and y-components Cx and Cy of vector ? Cx = 1 cm, Cy = –1 cm Cx= –3 cm, Cy = 1 cm Cx = –2 cm, Cy = 1 cm Cx= –4 cm, Cy = 2 cm Cx= –3 cm, Cy = –1 cm

17. What are the x- and y-components Cx and Cy of vector ? Cx = 1 cm, Cy = –1 cm Cx= –3 cm, Cy = 1 cm Cx = –2 cm, Cy = 1 cm Cx= –4 cm, Cy = 2 cm Cx= –3 cm, Cy = –1 cm

18. Chapter 4. Reading Quizzes

19. A ball is thrown upward at a 45° angle. In the absence of air resistance, the ball follows a • tangential curve. • sine curve. • parabolic curve. • linear curve.

20. A ball is thrown upward at a 45° angle. In the absence of air resistance, the ball follows a • tangential curve. • sine curve. • parabolic curve. • linear curve.

21. A hunter points his rifle directly at a coconut that he wishes to shoot off a tree. It so happens that the coconut falls from the tree at the exact instant the hunter pulls the trigger. Consequently, • the bullet passes above the coconut. • the bullet hits the coconut. • the bullet passes beneath the coconut. • This wasn’t discussed in Chapter 4.

22. A hunter points his rifle directly at a coconut that he wishes to shoot off a tree. It so happens that the coconut falls from the tree at the exact instant the hunter pulls the trigger. Consequently, • the bullet passes above the coconut. • the bullet hits the coconut. • the bullet passes beneath the coconut. • This wasn’t discussed in Chapter 4.

23. Projectile Motion

24. 2D Motion Concept Questions

25. This acceleration will cause the particle to • slow down and curve downward. • slow down and curve upward. • speed up and curve downward. • speed up and curve upward. • move to the right and down.

26. This acceleration will cause the particle to • slow down and curve downward. • slow down and curve upward. • speed up and curve downward. • speed up and curve upward. • move to the right and down.

27. Firing Balls I 1) it depends on how fast the cart is moving 2) it falls behind the cart 3) it falls in front of the cart 4) it falls right back into the cart 5) it remains at rest A small cart is rolling at constant velocity on a flat track. It fires a ball straight up into the air as it moves. After it is fired, what happens to the ball?

28. ConcepTest 3.4a Firing Balls I when viewed from train when viewed from ground 1) it depends on how fast the cart is moving 2) it falls behind the cart 3) it falls in front of the cart 4) it falls right back into the cart 5) it remains at rest A small cart is rolling at constant velocity on a flat track. It fires a ball straight up into the air as it moves. After it is fired, what happens to the ball? In the frame of reference of the cart, the ball only has a verticalcomponent of velocity. So it goes up and comes back down. To a ground observer, both the cart and the ball have the same horizontal velocity, so the ball still returns into the cart.

29. Dropping a Package 1) quickly lag behind the plane while falling 2) remain vertically under the plane while falling 3) move ahead of the plane while falling 4) not fall at all You drop a package from a plane flying at constant speed in a straight line. Without air resistance, the package will:

30. ConcepTest 3.5 Dropping a Package 1) quickly lag behind the plane while falling 2) remain vertically under the plane while falling 3) move ahead of the plane while falling 4) not fall at all You drop a package from a plane flying at constant speed in a straight line. Without air resistance, the package will: Both the plane and the package have the samehorizontalvelocity at the moment of release. They will maintainthis velocity in the x-direction, so they stay aligned. Follow-up: What would happen if air resistance were present?

31. Dropping the Ball I 1) the “dropped” ball 2) the “fired” ball 3) they both hit at the same time 4) it depends on how hard the ball was fired 5) it depends on the initial height From the same height (and at the same time), one ball is dropped and another ball is fired horizontally. Which one will hit the ground first?

32. Dropping the Ball I 1) the “dropped” ball 2) the “fired” ball 3) they both hit at the same time 4) it depends on how hard the ball was fired 5) it depends on the initial height From the same height (and at the same time), one ball is dropped and another ball is fired horizontally. Which one will hit the ground first? Both of the balls are falling vertically under the influence of gravity. They both fall from the same height.Therefore, they will hit the ground at the same time. The fact that one is moving horizontally is irrelevant – remember that the x and y motions are completely independent !! Follow-up: Is that also true if there is air resistance?

33. Dropping the Ball II 1) the “dropped” ball 2) the “fired” ball 3) neither – they both have the same velocity on impact 4) it depends on how hard the ball was thrown In the previous problem, which ball has the greater velocity at ground level?

34. Dropping the Ball II 1) the “dropped” ball 2) the “fired” ball 3) neither – they both have the same velocity on impact 4) it depends on how hard the ball was thrown In the previous problem, which ball has the greater velocity at ground level? Both balls have the same vertical velocity when they hit the ground (since they are both acted on by gravity for the same time). However, the “fired” ball also has a horizontal velocity. When you add the two components vectorially, the “fired” ball has a larger net velocity when it hits the ground.

35. Projectile 1) just after it is launched 2) at the highest point in its flight 3) just before it hits the ground 4) halfway between the ground and the highest point 5) speed is always constant A projectile is launched from the ground at an angle of 30o. At what point in its trajectory does this projectile have the least speed?

36. Projectile 1) just after it is launched 2) at the highest point in its flight 3) just before it hits the ground 4) halfway between the ground and the highest point 5) speed is always constant A projectile is launched from the ground at an angle of 30o. At what point in its trajectory does this projectile have the least speed? The speed is smallestat the highest point of its flight path because the y-component of the velocity is zero.