Vectors - 5 Steps to a 5 500 AP Physics Questions to Know by Test Day

5 Steps to a 5 500 AP Physics Questions to Know by Test Day (2012)

Chapter 1. Vectors

1. Add the following vectors and give the resultant vector: (5î+9ĵ), (6î-3ĵ), (2î-12ĵ).

(A) 31

(B) 14, 3, −10

(C) (13î-6ĵ)

(D) (13î+24ĵ)

(E) (14î+3ĵ-10ç)

2. Why are North, South, East, and West not vectors?

(A) They are vectors.

(B) They state a direction.

(C) They state a direction but not a magnitude.

(D) They are scalars.

(E) They have no reference coordinates.

3. A temperature is a scalar because

(A) it is a vector.

(B) it measures heat.

(C) it only has one dimension and two directions.

(D) it states a magnitude but not a direction.

(E) it is a qualitative measure.

4. What is the difference between velocity and speed?

(A) There is no difference.

(B) Velocity is a vector, and speed is a scalar.

(C) Speed is a vector, and velocity is a scalar.

(D) Speed states only a magnitude, and velocity states a magnitude and direction.

(E) Velocity states only a magnitude, and speed states a magnitude and direction.

5. Why can a vector be expressed in an R Φ system?

(A) It cannot be expressed in an R θ Φ system.

(B) It cannot be expressed because it has no x, y, z directions.

(C) It can be expressed because a magnitude is expressed by R and a direction by θ and Φ.

(D) It can be expressed because R θ Φ can be expressed as x, y, z components.

(E) It cannot be expressed because R θ Φ is only used in special cases.

6. What is the magnitude of this vector, 100. î-200.ĵ+1500.k?

(A) 1520

(B) 1516

(C) 1516.6

(D) 1800

(E) 1400

7. What is the angle made with the x axis by this vector, 1200.î-200.ĵ?

(A) 9°

(B) 80°

(C) 9.46°

(D) 80.5°

(E) .167 radians

8. What is the dot product of two vectors, A and B?

(A) |A|·|B|

(B) |A|·|B|·sinθ

(C) |A|·|B|·cosθ

(D) |A|·|B|·tan|·sinθ

(E) |A|·|B|arctan|·sinθ

9. What is the cross product of two vectors, A and B?

(A) |A|·|B|·cosθ

(B) |A|·|B|·cosθ directed perpendicular to the plane of A and B

(C) |A|·|B|·sinθ directed perpendicular to the plane of A and B

(D) |A|·|B|·sinθ directed perpendicular to the plane of A and B in the positive direction

(E) |A|·|B|·cosθ directed perpendicular to the plane of A and B in the negative direction

10. Which of the following is a scalar?

(A) Force

(B) Acceleration

(C) Velocity

(D) Moles

(E) Angular velocity

11. What are the x and y components of a vector with a magnitude of 50, directed 33° from the x axis?

(A) 27.23 and 41.93

(B) 50 and 50

(C) 27 and 42

(D) 42 and 27

(E) 41.93 and 27.23

12. What are the x, y, and z components of a vector with a magnitude of 58, directed 33° from the x axis and 120° from the z axis?

(A) 49.î + 32.ĵ - 29.k

(B) 42.î + 27.ĵ - 29.k

(C) 49.î + 27.ĵ - 29.k

(D) 42.î + 27.ĵ - 29.k

(E) 42.î - 27.ĵ + 29.k

13. What is the resultant vector after adding 12. î-20.ĵ+150.k, 52.î+43.ĵ-1.k, and −23.î-13.ĵ-61.k?

(A) 142.î+40.ĵ+136.k

(B) 41.î+10.ĵ+98.k

(C) −41.î-10.ĵ-98.k

(D) 188

(E) 133

14. If a hiker heads north for 2.0 miles, northeast for 3.0 miles, west for 2.0 miles, and then south for 3.0 miles, what vector describes his final position?

(A) The hiker is lost

(B) The hiker is 1.1 miles from his starting point

(C) 0.1 mi î+1.1 mi ĵ

(D) 2.0 mi î

(E) 1.0 mi ĵ

15. Which of the following is a vector?

(A) Time

(B) Distance

(C) Force

(D) Speed

(E) Direction

16. Why are vectors needed?

(A) To define a location

(B) To define a force or moment

(C) To define acceleration

(D) (A), (B), and (C)

(E) Only (A)

17. What angle does the following vector, 53.0î - 42.0ĵ + 29.0k, make with the x axis?

(A) 90°

(B) 54.2°

(C) 35.8°

(D) 52°

(E) 38.4°

18. What angle does the following vector, 53.0î - 42.0ĵ + 29.0k, make with the z axis?

(A) 23.2°

(B) 66.8°

(C) 38.4°

(D) 21.5°

(E) 68.5°

19. What is the product of a vector and a scalar?

(A) A scalar

(B) A vector

(C) A magnitude

(D) The same vector

(E) A different direction

20. What is the product of two vectors?

(A) The angle between the two vectors

(B) A vector and a scalar

(C) A scalar

(D) A scalar or a vector

(E) A vector

21. What is the dot product of 13.0î and −42.0î?

(A) 546.0

(B) −546.0

(C) 0.0

(D) 53.0î

(E) −53.0î

22. What is the cross product of 13.0î and −42.0î?

(A) 546.0

(B) −546.0

(C) 0.0

(D) 53.0î

(E) −53.0î

23. What is the right-hand rule for vector cross products?

(A) It defines how screws should turn.

(B) It defines the vector coordinate system.

(C) It defines the direction of the cross product vector.

(D) It defines the positive or negative direction of the cross product vector.

(E) It defines the perpendicular direction of the cross product.

24. What is the dot product of 13.0î and −42.0ĵ?

(A) 546.0

(B) −546.0

(C) 0.0

(D) 53.0î

(E) −53.0î

25. What is the cross product of 13.0î and −42.0ĵ?

(A) −546.0k

(B) 546.0k

(C) 0.0

(D) 53.0

(E) −53.0

26. Air traffic controllers give “vectors” to inform pilots of the direction (degrees of the compass) in which they should fly. Is this a correct use of vectors? Why or why not?

(A) Yes, because the direction and the speed of the plane make up a vector

(B) No, because they need to know the height of the plane

(C) Yes, because the pilots know the height and speed of the plane

(D) No, because the only information provided is a direction without a magnitude

(E) No, because compass degrees are not scalars

27. Which of the following is a true mathematical operation?

(A) A × B = B × A

(B) A + B = B + A

(C) A × (B · C)

(D) A · (B · C)

(E) A × (B × C) = (A × B) × C

28. Why is A ·(A×B) = 0 a mathematical operation?

(A) This is not a correct mathematical operation.

(B) A and B must be 0.

(C) The cross product gives a vector perpendicular to A and sin 90° = 0.

(D) The cross product gives a vector perpendicular to A and cos 90° = 0.

(E) Acrtan (A/B) = 0.

29. For the following vectors, provide their x, y, z components, dot product, and cross product. Vector A has a magnitude of 20 N and is directed 40° from the x axis, 50° from the y axis, and 30° from the z axis. Vector B has a magnitude of 30 N and is directed 120° from the x axis, 30° from the y axis, and 300° from the z axis.

30. In the constellation Ursa Major, or the Big Dipper, one star, Alkaid, forms the end of the dipper handle and Merak forms the outside bottom corner of the dipper bowl. Alkaid is 138 light years away from the Earth, and Merak is 77 light years away from the Earth. When viewed from the Earth, the two stars are 25.6° apart. How far is Alkaid from Merak?