Q: A vector has a magnitude of 10 m and points 30° above the x-axis. What are the x and y components of this vector?

$$x = 10 \cos(30^\circ) = 8.66\ \text{m},\ y = 10 \sin(30^\circ) = 5.0\ \text{m}$$

Q: Which trigonometric function would you use to find the angle $$\theta if $$you know the lengths of the opposite side and the hypotenuse in a right triangle?

$$\sin \theta = \frac{\text{opp}}{\text{hyp}}$$

Q: A vector $$\vec{A}$$ has a magnitude of 10 m and points in the direction $$60^\circ$$ above the x-axis. What is the y-component of $$\vec{A}$$?

$$A_y = 10 \sin(60^\circ) = 8.66\ \text{m}$$

Q: A vector $$\vec{C}$$ has components $$C_x = -6$$ and $$C_y = 8. $$What is the direction of $$\vec{C}$$ with respect to the x-axis?

$$\theta = \tan$$^{-1}$$\left(\frac{8}{-6}\right) = -53.1^\circ ($$measured from the x-axis)

Q: A vector $$\vec{D}$$ has a magnitude of 20 m and points at an angle of $$120^\circ$$ from the x-axis. What is the x-component of $$\vec{D}$$?

$$D_x = 20 \cos(120^\circ) = -10\ \text{m}$$

Question 1

Which of the following is a scalar quantity?

Accepted Answer

5 meters

Question 2

A vector has a magnitude of 10 m and points 30° above the x-axis. What are the x and y components of this vector?

Accepted Answer

$$x = 10 \cos(30^\circ) = 8.66\ 	ext{m},\ y = 10 \sin(30^\circ) = 5.0\ 	ext{m}$$

Question 3

Which equation correctly represents the Pythagorean Theorem as used in vector addition?

Accepted Answer

$$a^2$$ + $$b^2$$ = $$c^2$$

Question 4

If a vector $$\vec{A}$$ has components $$A_x = 3$$ and $$A_y = 4$$, what is the magnitude of $$\vec{A}$$?

Accepted Answer

$$\sqrt{3^2$ + 4^2$} = 5$$

Question 5

Which trigonometric function would you use to find the angle $$	heta if $$you know the lengths of the opposite side and the hypotenuse in a right triangle?

Accepted Answer

$$\sin 	heta = \frac{	ext{opp}}{	ext{hyp}}$$

Question 6

A vector $$\vec{B} is $$given as $$\vec{B} = 5\hat{i} + 12\hat{j}. $$What is the magnitude of $$\vec{B}$$?

Accepted Answer

$$\sqrt{5^2$ + 12^2$} = 13$$

Question 7

When adding two vectors that are perpendicular to each other, which method should you use to find the magnitude of the resultant vector?

Accepted Answer

Use the Pythagorean Theorem: $$C = \sqrt{A^2$ + B^2$}$$

Question 8

A vector $$\vec{A}$$ has a magnitude of 10 m and points in the direction $$60^\circ$$ above the x-axis. What is the y-component of $$\vec{A}$$?

Accepted Answer

$$A_y = 10 \sin(60^\circ) = 8.66\ 	ext{m}$$

Question 9

Which of the following statements about vectors is TRUE?

Accepted Answer

Vectors have both magnitude and direction.

Question 10

If you are given two vectors $$\vec{A}$$ and $$\vec{B}$$ that are not perpendicular or parallel, which method should you use to add them?

Accepted Answer

Resolve each vector into components and add the components.

Question 11

A vector $$\vec{C}$$ has components $$C_x = -6$$ and $$C_y = 8. $$What is the direction of $$\vec{C}$$ with respect to the x-axis?

Accepted Answer

$$	heta = 	an$$^{-1}$$\left(\frac{8}{-6}ight) = -53.1^\circ ($$measured from the x-axis)

Question 12

Which of the following best describes the unit vector $$\hat{i}$$?

Accepted Answer

A vector of magnitude 1 pointing in the positive x direction.

Question 13

If you subtract vector $$\vec{B}$$ from vector $$\vec{A}$$, which of the following is correct?

Accepted Answer

$$\vec{A} - \vec{B} is $$equivalent to adding $$\vec{A}$$ and $$-\vec{B}.$$

Question 14

A vector $$\vec{D}$$ has a magnitude of 20 m and points at an angle of $$120^\circ$$ from the x-axis. What is the x-component of $$\vec{D}$$?

Accepted Answer

$$D_x = 20 \cos(120^\circ) = -10\ 	ext{m}$$

Question 15

Which of the following is NOT a correct method for adding vectors?

Accepted Answer

Adding their magnitudes directly without considering direction.

Question 16

If a vector $$\vec{E}$$ has components $$E_x = 7$$ and $$E_y = -24$$, what is the magnitude of $$\vec{E}$$?

Accepted Answer

$$\sqrt{7^2$ + (-24)^2$} = 25$$

Question 17

Which trigonometric function is used to find the angle $$	heta if $$you know the adjacent and opposite sides of a right triangle?

Accepted Answer

$$	an 	heta = \frac{	ext{opp}}{	ext{adj}}$$

Question 18

A vector $$\vec{F} is $$described as $$\vec{F} = 8\hat{i} - 6\hat{j}. $$What is the direction of $$\vec{F}$$ with respect to the x-axis?

Accepted Answer

$$	heta = 	an$$^{-1}$$\left(\frac{-6}{8}ight) = -36.9^\circ$$

Question 19

When resolving a vector into x and y components, which of the following is a common mistake?

Accepted Answer

Assuming the x component always uses the cosine function regardless of the angle's position.

Vectors and Trigonometry in Physics: Structured Study Notes

Guida di studio - Domande di pratica

Study guide - Flashcard