$$\theta = \tan$$^{-1}$$\left(\frac{4}{3}\right)$$

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

Question 1

Which of the following best describes a vector quantity?

Accepted Answer

A quantity that has both magnitude and direction.

Question 2

Sam and Bill each walk 200 ft to the northeast from their respective front doors. Which statement is true about their displacement vectors?

Accepted Answer

Their displacement 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 hiker’s net displacement?

Accepted Answer

$$5$$ miles

Question 4

Given two vectors $$\vec{A}$$ and $$\vec{B} at $$right angles, how do you find the magnitude of their sum $$\vec{C} = \vec{A} + \vec{B}$$?

Accepted Answer

$$C = \sqrt{A^2$ + B^2$}$$

Question 5

A car’s velocity vector has components $$v_x = -6.0\ \mathrm{m/s}$$ and $$v_y = 4.0\ \mathrm{m/s}. $$What is the car’s speed?

Accepted Answer

$$7.2\ \mathrm{m/s}$$

Question 6

A hummingbird’s acceleration is $$6.0\ \mathrm{m/s^2$}$$, $$30^\circ$$ south of west. What are the $$x- $$and $$y-$$components of the acceleration?

Accepted Answer

$$a_x = -5.2\ \mathrm{m/s^2$},\ a_y = -3.0\ \mathrm{m/s^2$}$$

Question 7

Which of the following is the correct way to write a vector $$\vec{A} in $$terms of its components and unit vectors?

Accepted Answer

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

Question 8

If a vector $$\vec{B}$$ has components $$B_x = -2\ \mathrm{m}$$ and $$B_y = 3\ \mathrm{m}$$, in which quadrant does it point?

Accepted Answer

Quadrant II

Question 9

A vector $$\vec{C}$$ has components $$C_x = 3$$ and $$C_y = 4. $$What is the angle $$	heta it $$makes with the $$x-$$axis?

Accepted Answer

$$	heta = 	an$$^{-1}$$\left(\frac{4}{3}ight)$$

Question 10

Which of the following is a correct statement about the addition of vectors using the parallelogram rule?

Accepted Answer

The sum is the diagonal of the parallelogram formed by the two vectors.

Question 11

A GPS device uses which of the following to determine your position?

Accepted Answer

Satellite signals and the earth’s coordinate system.

Question 12

If $$\vec{D} = \vec{A} + \vec{B} + \vec{C}$$, how do you find the $$x-$$component $$D_x$$?

Accepted Answer

$$D_x = A_x + B_x + C_x$$

Question 13

A vector $$\vec{A}$$ 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 14

Which of the following is true about unit vectors $$\hat{i}$$ and $$\hat{j}$$?

Accepted Answer

They have magnitude 1 and point in the positive $$x- $$and $$y-$$directions, respectively.

Question 15

A vector $$\vec{B}$$ has components $$B_x = 3$$ and $$B_y = -4. $$What is the magnitude of $$\vec{B}$$?

Accepted Answer

$$5$$

Question 16

If a vector points left and down, what must you remember when writing its $$x- $$and $$y-$$components?

Accepted Answer

Insert minus signs for both components.

Question 17

Which of the following best describes the process of decomposing a vector?

Accepted Answer

Breaking a vector into two perpendicular vectors parallel to the coordinate axes.

Question 18

A vector $$\vec{C}$$ has components $$C_x = -4 cm $$and $$C_y = 2 cm. $$How can it be written using unit vectors?

Accepted Answer

$$\vec{C} = -4 \hat{i} + 2 \hat{j} cm$$

Question 19

Which formula gives the direction $$\phi of a $$vector $$\vec{C} in $$terms of its components?

Accepted Answer

$$\phi = 	an$$^{-1}$$\left(\frac{C_y}{C_x}ight)$$

Vectors and Coordinate Systems: Physics with Calculus Study Notes

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