Q: If a vector $\vec{A}$ makes an angle $\theta$ with the x-axis, what are its x and y components?

$A_x = |\vec{A}| \cos \theta$, $A_y = |\vec{A}| \sin \theta$

Q: A vector $\vec{R}$ has components $R_x = 6$ and $R_y = 8$. What is the direction of $\vec{R}$ with respect to the x-axis?

$\theta = \tan^{-1} \left( \frac{8}{6} \right)$

Question 1

Which of the following best describes a scalar quantity?

Accepted Answer

A quantity that is fully described by a single number (magnitude) and has no direction.

Question 2

Given two vectors $\vec{A}$ and $\vec{B}$ with components $\vec{A} = (3, 4)$ and $\vec{B} = (1, 2)$, what is the resultant vector $\vec{R} = \vec{A} + \vec{B}$?

Accepted Answer

$\vec{R} = (4, 6)$

Question 3

A rock is thrown straight up from the roof of a 100 m tall building with an initial velocity of $10 \ \mathrm{m/s}$. Neglecting air resistance, what is the maximum height above the ground the rock reaches? (Use $g = 9.8 \ \mathrm{m/s^2}$)

Accepted Answer

$105.1 \ \mathrm{m}$

Question 4

Which equation correctly gives the magnitude of a vector $\vec{A}$ with components $A_x$ and $A_y$?

Accepted Answer

$|\vec{A}| = \sqrt{A_x^2 + A_y^2}$

Question 5

A projectile is launched horizontally from a cliff with an initial speed of $v_0$. Which of the following statements is true about its vertical motion?

Accepted Answer

The vertical velocity increases linearly with time due to gravity.

Question 6

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

Accepted Answer

$A_x = |\vec{A}| \cos 	heta$, $A_y = |\vec{A}| \sin 	heta$

Question 7

A car moves 5 km east, then 12 km north. What is the magnitude of its net displacement?

Accepted Answer

$13 \ \mathrm{km}$

Question 8

Which of the following is NOT a property of vectors?

Accepted Answer

Vectors can be fully described by magnitude alone.

Question 9

A ball is dropped from rest from a height $h$. What is its velocity just before hitting the ground? (Neglect air resistance)

Accepted Answer

$v = \sqrt{2gh}$

Question 10

Which of the following best describes instantaneous acceleration?

Accepted Answer

The change in velocity over an infinitesimally small time interval.

Question 11

A vector $\vec{R}$ has components $R_x = 6$ and $R_y = 8$. What is the direction of $\vec{R}$ with respect to the x-axis?

Accepted Answer

$	heta = 	an^{-1} \left( \frac{8}{6} ight)$

Question 12

A stone is thrown horizontally from a cliff and lands 40 m away from the base after 2 s. What was its initial speed?

Accepted Answer

$20 \ \mathrm{m/s}$

Question 13

Which equation gives the vertical position $y$ of a projectile at time $t$ if it is launched with initial vertical velocity $v_{0y}$ from height $y_0$?

Accepted Answer

$y = y_0 + v_{0y} t - \frac{1}{2} g t^2$

Question 14

A vector $\vec{A}$ is represented by $\vec{A} = (A_x, A_y)$. If $A_x = 0$ and $A_y = -5$, what is the direction of $\vec{A}$?

Accepted Answer

$270^\circ$ (downward along the y-axis)

Question 15

Which of the following is a correct statement about the magnitude of a vector?

Accepted Answer

It is always a non-negative scalar.

Question 16

A projectile is launched at an angle $	heta$ with initial speed $v_0$. What is the formula for its initial vertical velocity component?

Accepted Answer

$v_{0y} = v_0 \sin 	heta$

Question 17

A vector $\vec{B}$ has a magnitude of $10$ and points at $60^\circ$ above the x-axis. What is its y-component?

Accepted Answer

$B_y = 10 \sin 60^\circ = 8.66$

Question 18

Which of the following is the correct formula for average velocity $\bar{v}$ over a time interval $\Delta t$?

Accepted Answer

$\bar{v} = \frac{\Delta x}{\Delta t}$

Question 19

A vector $\vec{C}$ has components $C_x = -3$ and $C_y = 4$. What is the magnitude of $\vec{C}$?

Accepted Answer

$5$

Vectors, Kinematics, and Free-Fall Motion: Physics Study Notes

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