Q: Which equation correctly finds the direction $$\theta of a $$resultant vector with components $$R_x$$ and $$R_y$$?

$$\theta = \tan$$^{-1}$$ \left( \frac{R_y}{R_x} \right)$$

Q: A boat heads $$8\ \mathrm{km}$$ north and then $$6\ \mathrm{km}$$ east. What is the direction of the resultant displacement from the starting point (relative to east)?

$$\tan$$^{-1}$$ \left( \frac{8}{6} \right)$$ north of east

Question 1

Which of the following quantities is a vector?

Accepted Answer

Velocity

Question 2

A treasure is buried 10 m from a tree. Why is this information insufficient to locate the treasure?

Accepted Answer

Because the direction is missing.

Question 3

Which of the following best describes a scalar quantity?

Accepted Answer

A quantity with only magnitude.

Question 4

Two vectors have magnitudes 5 m and 3 m. Which of the following could be the magnitude of their sum?

Accepted Answer

$$7\ \mathrm{m}$$

Question 5

If two vectors add to zero, which of the following must be true?

Accepted Answer

They have equal magnitudes and opposite directions.

Question 6

Given a vector $$\vec{A}$$ with magnitude $$A$$ and angle $$	heta$$ from the $$+x$$ axis, what is the $$y-$$component?

Accepted Answer

$$A \sin 	heta$$

Question 7

A vector $$\vec{C}$$ has a magnitude of $$4\ \mathrm{m}$$ and points $$30^\circ$$ east of south. What is the $$x-$$component of $$\vec{C} if $$east is the positive $$x-$$direction?

Accepted Answer

$$4 \sin 30^\circ$$

Question 8

Which component(s) of a vector change if the angle changes but the magnitude stays the same?

Accepted Answer

Both $$A_x$$ and $$A_y$$

Question 9

What is the resultant magnitude $$R$$ when two perpendicular vectors $$A = 3\ \mathrm{m}$$ and $$B = 4\ \mathrm{m}$$ are added?

Accepted Answer

$$R = 5\ \mathrm{m}$$

Question 10

Which equation correctly finds the direction $$	heta of a $$resultant vector with components $$R_x$$ and $$R_y$$?

Accepted Answer

$$	heta = 	an$$^{-1}$$ \left( \frac{R_y}{R_x} ight)$$

Question 11

A hiker walks $$5\ \mathrm{km}$$ east, then $$12\ \mathrm{km}$$ north. What is the magnitude of the displacement from the starting point?

Accepted Answer

$$13\ \mathrm{km}$$

Question 12

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

Accepted Answer

The resultant is always larger than either vector.

Question 13

Why do we use vector components in physics problems?

Accepted Answer

To break 2-D motion into two 1-D problems.

Question 14

A boat heads $$8\ \mathrm{km}$$ north and then $$6\ \mathrm{km}$$ east. What is the direction of the resultant displacement from the starting point (relative to east)?

Accepted Answer

$$	an$$^{-1}$$ \left( \frac{8}{6} ight)$$ north of east

Question 15

Which of the following best describes the graphical tail-to-tip method for vector addition?

Accepted Answer

Place the tail of the second vector at the tip of the first.

Question 16

If $$\vec{A} = 2\ \mathrm{m}$$ east and $$\vec{B} = 3\ \mathrm{m}$$ south, what is the magnitude of $$\vec{A} + \vec{B}$$?

Accepted Answer

$$\sqrt{13}\ \mathrm{m}$$

Question 17

Which of the following is a correct statement about the resultant of two vectors $$\vec{A}$$ and $$\vec{B}$$?

Accepted Answer

The resultant must be between $$||\vec{A}| - |\vec{B}||$$ and $$|\vec{A}| + |\vec{B}|.$$

Question 18

A vector has components $$A_x = 3$$ and $$A_y = 4. $$What is the magnitude of the vector?

Accepted Answer

$$5$$

Question 19

Which of the following is a real-world example where vector addition is necessary?

Accepted Answer

Finding the net force on a car at an intersection with wind blowing from the side.

2D Kinematics: Vectors – Concepts, Methods, and Applications

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