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

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

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

$$\sqrt{(100)^2$ + (50)^2$ - 2 \times 100 \times 50 \times \cos 45^\circ} = 74\,\text{m}$$

Q: A rabbit runs at $$10.0\,\text{m/s}$$, $$40.0^\circ$$ north of west. What is the $$x-$$component of its velocity?

$$-10.0 \times \cos 40.0^\circ = -7.66\,\text{m/s}$$

Q: Given a vector $$\vec{A}$$ with components $$A_x$$ and $$A_y$$, how do you find the direction angle $$\theta$$ relative to the $$x-$$axis?

$$\theta = \arctan \left( \frac{A_y}{A_x} \right)$$

Q: If $$\vec{B} = (-35.3\vec{i} + 35.3\vec{j})\,\text{m}$$ and $$\vec{A} = (100\vec{i})\,\text{m}$$, what is $$\vec{C} = \vec{A} + \vec{B}$$?

$$(64.7\vec{i} + 35.3\vec{j})\,\text{m}$$

Question 1

Which of the following best describes a vector quantity?

Accepted Answer

A quantity that has both magnitude and direction, such as velocity.

Question 2

Sam walks 200 ft northeast from his house. What is the magnitude of his displacement vector $$\vec{S}$$?

Accepted Answer

$$|\vec{S}| = 200\,	ext{ft}$$

Question 3

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

Accepted Answer

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

Question 4

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

Accepted Answer

$$\sqrt{(100)^2$ + (50)^2$ - 2 	imes 100 	imes 50 	imes \cos 45^\circ} = 74\,	ext{m}$$

Question 5

Which rule allows you to find the sum of two vectors by drawing them with their tails together and constructing a parallelogram?

Accepted Answer

The parallelogram rule

Question 6

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

Accepted Answer

$$|\vec{A}| = 5$$

Question 7

A rabbit runs at $$10.0\,	ext{m/s}$$, $$40.0^\circ$$ north of west. What is the $$x-$$component of its velocity?

Accepted Answer

$$-10.0 	imes \cos 40.0^\circ = -7.66\,	ext{m/s}$$

Question 8

Given a vector $$\vec{A}$$ with components $$A_x$$ and $$A_y$$, how do you find the direction angle $$	heta$$ relative to the $$x-$$axis?

Accepted Answer

$$	heta = \arctan \left( \frac{A_y}{A_x} ight)$$

Question 9

Which of the following is a correct expression for the decomposition of a vector $$\vec{A} in $$terms of unit vectors?

Accepted Answer

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

Question 10

If $$\vec{B} = (-35.3\vec{i} + 35.3\vec{j})\,	ext{m}$$ and $$\vec{A} = (100\vec{i})\,	ext{m}$$, what is $$\vec{C} = \vec{A} + \vec{B}$$?

Accepted Answer

$$(64.7\vec{i} + 35.3\vec{j})\,	ext{m}$$

Question 11

Which statement about unit vectors is correct?

Accepted Answer

Unit vectors have a magnitude of 1 and define the direction of coordinate axes.

Question 12

A vector $$\vec{D}$$ has components $$D_x = -4 cm $$and $$D_y = 2 cm. $$What quadrant does $$\vec{D}$$ point toward?

Accepted Answer

Second quadrant

Question 13

If you tilt the axes of a coordinate system, which property must remain true?

Accepted Answer

The axes must remain perpendicular to each other.

Question 14

Which operation is performed by adding the $$x- $$and $$y-$$components of vectors separately?

Accepted Answer

Algebraic addition of vectors

Question 15

A GPS system uses coordinate axes to determine your position. What is the primary purpose of a coordinate system in physics?

Accepted Answer

To artificially impose a grid for describing positions and directions.

Question 16

If $$\vec{A}$$ has a magnitude $$A$$ and makes an angle $$	heta$$ with the $$x-$$axis, what are its components?

Accepted Answer

$$A_x = A \cos 	heta$$, $$A_y = A \sin 	heta$$

Question 17

A vector $$\vec{F}$$ has components $$F_x = 0$$ and $$F_y = -5. $$Which direction does $$\vec{F}$$ point?

Accepted Answer

Negative y-direction

Question 18

Which of the following is NOT a vector quantity?

Accepted Answer

Temperature

Question 19

A vector $$\vec{G} is $$written as $$2\vec{i} - 4\vec{j}. $$What is its magnitude?

Accepted Answer

$$\sqrt{2^2$ + (-4)^2$} = \sqrt{20} = 4.47$$

Vectors and Coordinate Systems – Study Notes

Study Guide - Practice Questions

Study Guide - Flashcards