Question 1

Given the vector $$ \vec{A}  in $$image 1 has a magnitude of 8.0 m and points directly downward along the negative y-axis, what are its x and y components?

Accepted Answer

$$A_x = 0, \quad A_y = -8.0$$

Question 2

For vector $$ \vec{B}  in $$image 1, which has a magnitude of 15.0 m and is oriented 30° above the positive x-axis, what is the correct expression for its x-component?

Accepted Answer

$$B_x = 15.0 \cos 30^\circ$$

Question 3

What is the y-component of vector $$ \vec{C}  in $$image 1, given its magnitude is 12.0 m and it is 25° below the negative x-axis?

Accepted Answer

$$C_y = -12.0 \sin 25^\circ$$

Question 4

If vectors $$ \vec{A} $$, $$ \vec{B} $$, and $$ \vec{C}  in $$image 2 are added head-to-tail, which vector equation correctly represents the resultant $$ \vec{R} $$?

Accepted Answer

$$\vec{R} = \vec{A} + \vec{B} + \vec{C}$$

Question 5

In image 3, what is the x-component of vector $$ \vec{A}  (100.0 N$$, 30° above the x-axis)?

Accepted Answer

$$A_x = 100.0 \cos 30^\circ$$

Question 6

Which of the following best describes the process for finding the magnitude of the resultant vector $$ \vec{R} $$ when adding three vectors $$ \vec{A} $$, $$ \vec{B} $$, and $$ \vec{C} $$ given in component form?

Accepted Answer

$$|\vec{R}| = \sqrt{(A_x + B_x + C_x)^2$ + (A_y + B_y + C_y)^2$}$$

Question 7

A force vector $$ \vec{F} $$ has components $$F_x = 60.0 N $$and $$F_y = 80.0 N. $$What is the magnitude of $$ \vec{F} $$?

Accepted Answer

$$|\vec{F}| = \sqrt{60.0^2$ + 80.0^2$} = 100.0 N$$

Question 8

If vector $$ \vec{D}  in $$image 1 has a magnitude of 10.0 m and is 53° above the negative x-axis, what is the correct expression for its x-component?

Accepted Answer

$$D_x = -10.0 \cos 53^\circ$$

Question 9

A vector $$ \vec{V} $$ makes an angle $$	heta$$ with the positive x-axis. Which formula gives the y-component of $$ \vec{V} $$?

Accepted Answer

$$V_y = V \sin 	heta$$

Question 10

In image 3, if you want to find the net force acting at point O by adding vectors $$ \vec{A} $$, $$ \vec{B} $$, and $$ \vec{C} $$, what is the first step?

Accepted Answer

Resolve each vector into its x and y components.

Question 11

A vector $$ \vec{P} $$ has components $$P_x = -20$$ and $$P_y = 20. $$What is the direction of $$ \vec{P} $$ relative to the positive x-axis?

Accepted Answer

$$135^\circ$$

Question 12

Which of the following statements about vector addition is correct?

Accepted Answer

The resultant vector is independent of the order in which vectors are added.

Question 13

If a force vector $$ \vec{F}  is $$doubled in magnitude but its direction remains unchanged, what happens to its x and y components?

Accepted Answer

Both components are doubled.

Question 14

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

Accepted Answer

$$Q_y = 10 \sin 60^\circ$$

Question 15

Which of the following is a correct method to subtract vector $$ \vec{B} $$ from vector $$ \vec{A} $$?

Accepted Answer

$$\vec{A} - \vec{B}$$

Question 16

If the resultant of two vectors is zero, what can you conclude about the vectors?

Accepted Answer

They are equal in magnitude and opposite in direction.

Vectors: Representation, Addition, and Components

스터디 가이드 - 연습 문제

학습 가이드 - 플래시카드