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

스터디 가이드 - 연습 문제

학습 가이드 - 플래시카드