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

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

Q: Given vectors $$\vec{A}$$ and $$\vec{B}$$, both at right angles, what is the direction $$\theta of $$the resultant vector $$\vec{C}$$ with respect to $$\vec{A}$$?

$$\theta = \tan$$^{-1}$$\left(\frac{B}{A}\right)$$

Question 1

Which of the following is a correct definition of a vector quantity?

Accepted Answer

A quantity that has both magnitude and direction.

Question 2

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

Accepted Answer

$$\vec{S} = 200\ \mathrm{ft}$$

Question 3

A hiker walks 5 miles east and then 5 miles north. What is the magnitude of the net displacement?

Accepted Answer

$$\sqrt{5^2$ + 5^2$} = 7.07\ \mathrm{miles}$$

Question 4

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

Accepted Answer

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

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

Parallelogram rule

Question 6

Given vectors $$\vec{A}$$ and $$\vec{B}$$, both at right angles, what is the direction $$	heta of $$the resultant vector $$\vec{C}$$ with respect to $$\vec{A}$$?

Accepted Answer

$$	heta = 	an$$^{-1}$$\left(\frac{B}{A}ight)$$

Question 7

If a vector $$\vec{V}$$ has components $$V_x = -7.66\ \mathrm{m/s}$$ and $$V_y = 6.43\ \mathrm{m/s}$$, what is its magnitude?

Accepted Answer

$$\sqrt{(-7.66)^2$ + (6.43)^2$} = 10.0\ \mathrm{m/s}$$

Question 8

Which of the following is a unit vector in the positive y-direction?

Accepted Answer

$$\vec{j}$$

Question 9

A vector $$\vec{A}$$ has components $$A_x = 3$$ and $$A_y = 4. $$What is the vector's magnitude and direction?

Accepted Answer

Magnitude: $$5$$, Direction: $$53.1^\circ$$ above x-axis

Question 10

Which of the following best describes the process of decomposing a vector into its components?

Accepted Answer

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

Question 11

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

Accepted Answer

$$-(10.0\ \mathrm{m/s}) \cos 40.0^\circ = -7.66\ \mathrm{m/s}$$

Question 12

Which method is most efficient for adding several vectors algebraically?

Accepted Answer

Add the x- and y-components separately.

Question 13

If $$\vec{A} = 4\vec{i} + 3\vec{j}$$ and $$\vec{B} = -2\vec{i} + 5\vec{j}$$, what is $$\vec{C} = \vec{A} + \vec{B}$$?

Accepted Answer

$$2\vec{i} + 8\vec{j}$$

Question 14

A vector $$\vec{D}$$ has components $$D_x = -3 cm $$and $$D_y = 1 cm. $$Which direction does it point?

Accepted Answer

Left and up

Question 15

Which of the following is true about the zero vector $$\vec{0}$$?

Accepted Answer

It has zero length and no direction.

Question 16

If a vector $$\vec{F} is $$decomposed into components $$F_x$$ and $$F_y$$, which formula gives its magnitude?

Accepted Answer

$$|\vec{F}| = \sqrt{F_x^2$ + F_y^2$}$$

Question 17

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

Accepted Answer

Coordinate systems

Question 18

If you tilt the axes of your coordinate system, which property remains unchanged?

Accepted Answer

The axes remain perpendicular to each other.

Question 19

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

Accepted Answer

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

Vectors and Coordinate Systems – Study Notes

Guida di studio - Domande di pratica

Study guide - Flashcard