Q: A bird flies 100 m due east, then 50 m northwest (45° north of west). What is the magnitude of the bird’s net displacement?

$$\sqrt{100^2$ + 50^2$ - 2 \times 100 \times 50 \times \cos(135^\circ)}$$

Q: A rabbit runs at 10.0 m/s, 40.0° north of west. What is the x-component of its velocity (east is positive x)?

$$-10.0 \times \cos(40.0^\circ) m/s$$

Q: Given a vector $$\vec{B}$$ with components $$B_x = 4$$ and $$B_y = -3$$, what is the direction angle $$\theta$$ relative to the positive x-axis?

$$\theta = \arctan\left(\frac{-3}{4}\right)$$

Q: A force of 720 N acts at 15° to the humerus, which is tilted 30° below horizontal. What is the component of force parallel to the bone?

$$720 \times \cos(15^\circ) N$$

Question 1

Which of the following statements best describes a vector quantity?

Accepted Answer

A quantity that has both magnitude and direction.

Question 2

Two hikers start from different locations but each walks 5 km northeast. Which statement is true about their displacement vectors?

Accepted Answer

The vectors are equal because they have the same magnitude and direction.

Question 3

A hiker walks 4 miles east and then 3 miles north. What is the magnitude of the net displacement?

Accepted Answer

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

Question 4

A bird flies 100 m due east, then 50 m northwest (45° north of west). What is the magnitude of the bird’s net displacement?

Accepted Answer

$$\sqrt{100^2$ + 50^2$ - 2 	imes 100 	imes 50 	imes \cos(135^\circ)}$$

Question 5

Which method can be used to add two vectors graphically?

Accepted Answer

Tip-to-tail rule

Question 6

A vector $$\vec{A}$$ has components $$A_x = -3$$ and $$A_y = 2. $$What is the magnitude of $$\vec{A}$$?

Accepted Answer

$$\sqrt{(-3)^2$ + 2^2$} = \sqrt{9 + 4} = \sqrt{13}$$

Question 7

If a vector points left and down in a standard xy-coordinate system, what can be said about its x- and y-components?

Accepted Answer

Both components are negative.

Question 8

A rabbit runs at 10.0 m/s, 40.0° north of west. What is the x-component of its velocity (east is positive x)?

Accepted Answer

$$-10.0 	imes \cos(40.0^\circ) m/s$$

Question 9

Given a vector $$\vec{B}$$ with components $$B_x = 4$$ and $$B_y = -3$$, what is the direction angle $$	heta$$ relative to the positive x-axis?

Accepted Answer

$$	heta = \arctan\left(\frac{-3}{4}ight)$$

Question 10

Which of the following is a unit vector?

Accepted Answer

$$\hat{i}$$

Question 11

A vector $$\vec{C} is $$written as $$\vec{C} = 3\hat{i} - 4\hat{j}. $$What is the magnitude of $$\vec{C}$$?

Accepted Answer

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

Question 12

A force of 720 N acts at 15° to the humerus, which is tilted 30° below horizontal. What is the component of force parallel to the bone?

Accepted Answer

$$720 	imes \cos(15^\circ) N$$

Question 13

If a vector $$\vec{D}$$ has components $$D_x = -4 cm $$and $$D_y = 2 cm$$, which quadrant does it point to?

Accepted Answer

Quadrant II

Question 14

Which equation correctly expresses the vector $$\vec{A} in $$terms of its components and unit vectors?

Accepted Answer

$$\vec{A} = A_x \hat{i} + A_y \hat{j}$$

Question 15

A car’s velocity vector has components $$v_x = 5 m/s $$and $$v_y = -12 m/s. $$What is the speed of the car?

Accepted Answer

$$\sqrt{5^2$ + (-12)^2$} = 13 m/s$$

Question 16

Which of the following is NOT a property of vector addition?

Accepted Answer

The sum of two vectors is always a scalar.

Question 17

A vector $$\vec{E}$$ has a magnitude of 10 units and points 60° above the positive x-axis. What are its x- and y-components?

Accepted Answer

$$E_x = 10 	imes \cos(60^\circ)$$, $$E_y = 10 	imes \sin(60^\circ)$$

Question 18

If you tilt the axes of your coordinate system, what remains true?

Accepted Answer

The axes remain perpendicular to each other.

Question 19

A vector $$\vec{F} is $$decomposed into $$F_x = 6$$ and $$F_y = 8. $$What is the direction angle $$	heta$$ relative to the positive x-axis?

Accepted Answer

$$	heta = \arctan\left(\frac{8}{6}ight)$$

Question 20

A GPS uses satellite signals to determine your position. Which concept from this chapter is most directly related to this process?

Accepted Answer

Coordinate systems

Chapter 3: Vectors and Coordinate Systems – Study Notes

Study Guide - Practice Questions

Study Guide - Flashcards