Q: A hiker walks 5 km west, then 12 km south. What is the direction of the net displacement vector relative to west?

$$\tan$$^{-1}$$\left(\frac{12}{5}\right)$$ south of west

Q: A velocity vector $$\vec{v}$$ has components $$v_x = 3\ \mathrm{m/s}$$ and $$v_y = -4\ \mathrm{m/s}. $$What is the direction of $$\vec{v}$$ relative to the positive x-axis?

$$\tan$$^{-1}$$\left(\frac{-4}{3}\right)$$ below the x-axis

Q: A vector $$\vec{A} is $$decomposed into components $$A_x = -7$$ and $$A_y = -24. $$What is the angle $$\theta ($$measured counterclockwise from the positive x-axis) of $$\vec{A}$$?

$$\theta = 180^\circ + \tan$$^{-1}$$\left(\frac{24}{7}\right)$$

Question 1

A rescue drone flies 120 m due north, then 160 m due east. What is the magnitude of its net displacement from the starting point?

Accepted Answer

$$280\ \mathrm{m}$$

Question 2

Which of the following statements about vectors is correct?

Accepted Answer

A vector is a quantity with both magnitude and direction.

Question 3

A vector $$\vec{A}$$ has components $$A_x = -6$$ and $$A_y = 8. $$What is the magnitude of $$\vec{A}$$?

Accepted Answer

$$10$$

Question 4

A hiker walks 5 km west, then 12 km south. What is the direction of the net displacement vector relative to west?

Accepted Answer

$$	an$$^{-1}$$\left(\frac{12}{5}ight)$$ south of west

Question 5

Which of the following is NOT a property of unit vectors?

Accepted Answer

They can have any magnitude.

Question 6

A velocity vector $$\vec{v}$$ has components $$v_x = 3\ \mathrm{m/s}$$ and $$v_y = -4\ \mathrm{m/s}. $$What is the direction of $$\vec{v}$$ relative to the positive x-axis?

Accepted Answer

$$	an$$^{-1}$$\left(\frac{-4}{3}ight)$$ below the x-axis

Question 7

A force vector $$\vec{F}$$ has a magnitude of $$50\ \mathrm{N}$$ and points $$30^\circ$$ above the positive x-axis. What are its x- and y-components?

Accepted Answer

$$F_x = 50\cos 30^\circ$$, $$F_y = 50\sin 30^\circ$$

Question 8

A vector $$\vec{A} is $$decomposed into components $$A_x = -7$$ and $$A_y = -24. $$What is the angle $$	heta ($$measured counterclockwise from the positive x-axis) of $$\vec{A}$$?

Accepted Answer

$$	heta = 180^\circ + 	an$$^{-1}$$\left(\frac{24}{7}ight)$$

Question 9

A rabbit runs at $$12.0\ \mathrm{m/s}$$, $$50^\circ$$ north of west. What is the x-component of its velocity if the positive x-axis points east?

Accepted Answer

$$-12.0\cos 50^\circ$$

Question 10

A muscle pulls on a bone with a force of $$800\ \mathrm{N} at$$ $$20^\circ to $$the bone. What is the component of the force perpendicular to the bone?

Accepted Answer

$$800\sin 20^\circ$$

Question 11

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

Accepted Answer

Breaking it into pieces parallel to the axes.

Question 12

A car’s velocity vector is $$\vec{v} = -5\hat{i} + 12\hat{j}\ \mathrm{m/s}. $$What is the car’s speed?

Accepted Answer

$$13\ \mathrm{m/s}$$

Question 13

If a vector $$\vec{A} is $$multiplied by a scalar $$c = -2$$, what happens to its components?

Accepted Answer

Each component is multiplied by $$-2.$$

Question 14

A GPS uses satellite signals to determine your position in which type of system?

Accepted Answer

A coordinate system

Question 15

Which of the following is true about the addition of vectors?

Accepted Answer

The order of addition does not matter.

Question 16

A vector $$\vec{B}$$ has components $$B_x = 0$$ and $$B_y = -9. $$Which direction does $$\vec{B}$$ point?

Accepted Answer

Negative y-direction

Question 17

A displacement vector is $$\vec{d} = 6\hat{i} - 8\hat{j}\ \mathrm{m}. $$What is the magnitude of $$\vec{d}$$?

Accepted Answer

$$10\ \mathrm{m}$$

Question 18

If a vector points left and down, what must you do when writing its components?

Accepted Answer

Insert minus signs for both x and y components.

Question 19

A vector $$\vec{C}$$ has a magnitude of $$15$$ and points $$60^\circ$$ below the positive x-axis. What is the y-component of $$\vec{C}$$?

Accepted Answer

$$-15\sin 60^\circ$$

Question 20

Which of the following is a correct way to write a vector in terms of its components and unit vectors?

Accepted Answer

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

Vectors and Coordinate Systems: Study Notes

스터디 가이드 - 연습 문제

학습 가이드 - 플래시카드