Call Now to Set Up Tutoring:

(888) 888-0446

AP Physics 1 : Motion in Two Dimensions

Study concepts, example questions & explanations for AP Physics 1

Create An Account

All AP Physics 1 Resources

7 Diagnostic Tests 170 Practice Tests Question of the Day Flashcards Learn by Concept

Example Questions

Example Question #21 : Motion In Two Dimensions

An archer fires an arrow horizontally off a 60 meter high castle wall at a speed of $200\frac{m}{s}$ . What is the closest you could stand to the castle wall without fear of being hit?

$g=10\frac{m}{s^2}$

Possible Answers:

823m

540m

1000m

575m

693m

Correct answer:

693m

Explanation:

Find the time the object is airborne by solving for t in the equation:

$\Delta x=V_{0}t+.5at^2$

Then, multiply the time in the air by the initial velocity to get the range of the projectile. Note that the initial velocity is zero in the y-direction.

$t=\sqrt{\frac{2 \Delta y}{a}}=3.46s$

$Range= V_{0}*t=200\frac{m}{s}*3.46s=693m$

Report an Error

Example Question #351 : Newtonian Mechanics

A 100 N force pushes a 15 kg block, from rest, 60 cm across a frictionless table that is 85 cm above the floor. If the force stops acting on the block when it leaves the table, calculate how far $\left(\Delta x \right )$ the block lands from the table.

Possible Answers:

0.83 m

2.83 m

0.42 m

.49 m

1.19 m

Correct answer:

1.19 m

Explanation:

This is a two-part problem. First, we need to know how fast the block is moving in the horizontal direction when it leaves the table. This can be calculated by using a kinematic equation, combined with Newton's second law.

$V_f=\sqrt{V_i^2+2a\Delta x}$

$V_f=\sqrt{0+2\left(\frac{F}{m} \right ) \Delta x}$

$V_f=\sqrt{\frac{2(100N)(.60m)}{15kg}}=2.83\frac{m}{s}$

Now that we know how fast the block is moving horizontally, we need to know how long the block will be in air before hitting the ground. This is found by considering the equations of motion for an object falling from rest:

$0=-\frac{1}{2}gt^2+h \Rightarrow t=\sqrt{\frac{2h}{g}}$

$t=\sqrt{\frac{2(.85m)}{9.81\frac{m}{s^2}}}=0.42s$

Lastly, we find the horizontal distance by:

$\Delta x = vt = 2.83 \frac{m}{s}.0.42s=1.19 m$

Report an Error

Example Question #21 : Motion In Two Dimensions

A ball is thrown at a velocity $\vec{v}=\left (10\hat{i}+6\hat{j} \right )\frac{m}{s}$ . What is the speed of the ball?

Possible Answers:

$10\frac{m}{s}$

$4\frac{m}{s}$

$11.66\frac{m}{s}$

$6\frac{m}{s}$

Correct answer:

$11.66\frac{m}{s}$

Explanation:

If a vector is in the form $\vec{r}=a\hat{i}+b\hat{j}$ , the magnitude of a vector, $\left | \vec{r} \right |$ ,is found by using the equation $\left |\vec{r} \right |=\sqrt{a^{2}+b^{2}}$ .

Speed is the magnitude of the velocity vector. Given the velocity vector $\vec{v}=\left (10\hat{i}+6\hat{j} \right )\frac{m}{s}$ , the speed of the ball is:

$\left |\vec{v} \right |=\sqrt{10^{2}+6^{2}}=\sqrt{136}\approx11.66\frac{m}{s}$

Report an Error

Example Question #21 : Motion In Two Dimensions

An ant is digging at a velocity $\vec{v}=\left (7\hat{i}-5\hat{j} \right )\frac{mm}{s}$ into the Earth. What is the speed of the ant?

Possible Answers:

$5\frac{mm}{s}$

$8.60\frac{mm}{s}$

$7\frac{mm}{s}$

$2\frac{mm}{s}$

Correct answer:

$8.60\frac{mm}{s}$

Explanation:

If a vector is in the form $\vec{r}=a\hat{i}+b\hat{j}$ , the magnitude of a vector, $\left | \vec{r} \right |$ ,is found by using the equation $\left |\vec{r} \right |=\sqrt{a^{2}+b^{2}}$ .

Speed is the magnitude of the velocity vector. Given the velocity vector:

$\vec{v}=\left (7\hat{i}-5\hat{j} \right )\frac{mm}{s}$

The speed of the ant is:

$\left |\vec{v} \right |=\sqrt{7^{2}+(-5)^{2}}=\sqrt{49+25}=\sqrt{74}\approx8.60\frac{mm}{s}$

Report an Error

Example Question #111 : Linear Motion And Momentum

An ant is digging at a velocity $\vec{v}=\left (7\hat{i}-5\hat{j} \right )\frac{mm}{s}$ in the Earth. In what direction is the ant digging?

Possible Answers:

$59^{\circ}$ right of vertical

$59^{\circ}$ left of vertical

$54.5^{\circ}$ below the horizon

$54.5^{\circ}$ above the horizon

Correct answer:

$54.5^{\circ}$ below the horizon

Explanation:

A two-dimensional vector comes in the form $\vec{r}=a\hat{i}+b\hat{j}$ . The direction of the vector is found using the equation:

$\theta=tan^{-1}\left ( \frac{b}{a}\right )$

For this problem:

$\theta=tan^{-1}\left ( \frac{-7}{5}\right )\approx-54.5^{\circ}$

The ant is digging at an angle $54.5^{\circ}$ below the horizon.

Report an Error

Example Question #111 : Linear Motion And Momentum

A rollercoaster car is sliding down an incline at a velocity $\vec{v}=\left (-15\hat{i}-25\hat{j} \right )\frac{m}{s}$ . What is the speed of the rollercoaster car?

Possible Answers:

$25\frac{m}{s}$

$15\frac{m}{s}$

$10\frac{m}{s}$

$29.15\frac{m}{s}$

Correct answer:

$29.15\frac{m}{s}$

Explanation:

If a vector is in the form $\vec{r}=a\hat{i}+b\hat{j}$ , the magnitude of a vector, $\left | \vec{r} \right |$ ,is found by using the equation $\left |\vec{r} \right |=\sqrt{a^{2}+b^{2}}$ .

Speed is the magnitude of the velocity vector. Given the velocity vector:

$\vec{v}=\left (-15\hat{i}-25\hat{j} \right )\frac{m}{s}$

The speed of the rollercoaster car is:

$\left |\vec{v} \right |=\sqrt{(-15)^{2}+(-25)^{2}}=\sqrt{225+625}=\sqrt{850}\approx29.15\frac{m}{s}$

Report an Error

Example Question #352 : Newtonian Mechanics

A car travels east, south, then west. What is the magnitude of the displacement of the car?

Possible Answers:

11m

8.54m

Correct answer:

8.54m

Explanation:

To find the magnitude of the displacement of the car, we must represent each velocity of the car as a vector. We will then add the vectors. Finally, we will find the magnitude of the resulting velocity vector, which will give us speed.

The car first travels east , represented as a vector: $\vec{r}=\left (7\hat{i} \right )m$

The car then travels south , represented as a vector: $\vec{r}=\left (-8\hat{j} \right )m$

The car finally travels west , represented as a vector: $\vec{r}=\left (-4\hat{i} \right )m$

Adding the vectors together gives us the displacement of the car:

$\vec{r}=\left (7\hat{i}-8\hat{j}-4\hat{i} \right )m=\left (3\hat{i}-8\hat{j} \right )m$

If a vector is in the form $\vec{r}=a\hat{i}+b\hat{j}$ , its magnitude, $\left | \vec{r} \right |$ , is found by using the equation $\left |\vec{r} \right |=\sqrt{a^{2}+b^{2}}$

Given the displacement vector: $\vec{r}=\left (3\hat{i}-8\hat{j} \right )m$ , the magnitude of the displacement vector is:

$\left |\vec{r} \right |=\sqrt{3^{2}+(-8)^{2}}=\sqrt{9+64}=\sqrt{73}\approx8.54m$

Report an Error

Example Question #22 : Motion In Two Dimensions

A car travels east, south, then west. What is the direction of the displacement of the car?

Possible Answers:

$20.6^{\circ}$ below horizontal

$20.6^{\circ}$ above horizontal

$20.6^{\circ}$ left of vertical

$20.6^{\circ}$ right of vertical

Correct answer:

$20.6^{\circ}$ below horizontal

Explanation:

A two-dimensional vector comes in the form $\vec{r}=a\hat{i}+b\hat{j}$ . The angle of the vector is found using the equation:

$\theta=tan^{-1}\left ( \frac{b}{a}\right )$

For this problem, the displacement vector is:

$\vec{r}=\left (3\hat{i}-8\hat{j} \right )m$

The angle of displacement is:

$\theta=tan^{-1}\left ( \frac{3}{-8}\right )\approx-20.6^{\circ}$

The car is traveling $20.6^{\circ}$ below horizontal.

Report an Error

Example Question #22 : Motion In Two Dimensions

A boat is crossing a river is traveling east at $7\frac{m}{s}$ . The current of the river is traveling north at $3\frac{m}{s}$ . At what angle is the boat traveling?

Possible Answers:

$82.4^{\circ}$ below horizontal

$23.2^{\circ}$ above horizontal

$82.4^{\circ}$ above horizontal

$23.2^{\circ}$ below horizontal

Correct answer:

$23.2^{\circ}$ above horizontal

Explanation:

A two-dimensional vector comes in the form $\vec{r}=a\hat{i}+b\hat{j}$ . The angle of the vector is found using the equation:

$\theta=tan^{-1}\left ( \frac{b}{a}\right )$

For this problem, the velocity vector is: $\vec{v}=\left (7\hat{i}+3\hat{j} \right )\frac{m}{s}$

The angle of the boat is:

$\theta=tan^{-1}\left ( \frac{3}{7}\right )\approx23.2^{\circ}$

The boat is traveling $23.2^{\circ}$ above horizontal.

Report an Error

Example Question #353 : Newtonian Mechanics

A ball is thrown at a velocity $\vec{v}=\left (10\hat{i}+6\hat{j} \right)\frac{m}{s}$ . What is the direction of the ball (the angle at which the ball is thrown)?

Possible Answers:

$9^{\circ}$ left of vertical

$9^{\circ}$ right of vertical

$59^{\circ}$ above the horizon

$59^{\circ}$ below the horizon

Correct answer:

$59^{\circ}$ above the horizon

Explanation:

A two-dimensional vector comes in the form $\vec{r}=a\hat{i}+b\hat{j}$ . The direction of the vector is found using the equation:

$\theta=tan^{-1}\left ( \frac{b}{a}\right )$

For this problem:

$\theta=tan^{-1}\left ( \frac{10}{6}\right )\approx59^{\circ}$

The ball is thrown $59^{\circ}$ above the horizon.

Report an Error

View AP Physics 1 Tutors

Yousef
Certified Tutor

University of Massachusetts-Lowell, Doctor of Philosophy, Physics.

View AP Physics 1 Tutors

Gregory
Certified Tutor

Pennsylvania State University-Main Campus, Bachelor of Science, Chemical Engineering. Carnegie Mellon University, Doctor of P...

View AP Physics 1 Tutors

Muhammad
Certified Tutor

The University of Texas at Dallas, Bachelor of Science, Mechanical Engineering.

All AP Physics 1 Resources

7 Diagnostic Tests 170 Practice Tests Question of the Day Flashcards Learn by Concept

Popular Subjects

GMAT Tutors in Dallas Fort Worth, GRE Tutors in Phoenix, French Tutors in Los Angeles, Physics Tutors in Seattle, ACT Tutors in Phoenix, SSAT Tutors in San Francisco-Bay Area, Reading Tutors in Philadelphia, Reading Tutors in Houston, GMAT Tutors in Atlanta, ISEE Tutors in Phoenix

Popular Courses & Classes

ACT Courses & Classes in Los Angeles, MCAT Courses & Classes in Boston, LSAT Courses & Classes in San Diego, GMAT Courses & Classes in San Francisco-Bay Area, ACT Courses & Classes in Miami, SSAT Courses & Classes in New York City, GRE Courses & Classes in Phoenix, ACT Courses & Classes in New York City, MCAT Courses & Classes in Los Angeles, Spanish Courses & Classes in San Francisco-Bay Area

Popular Test Prep

SAT Test Prep in San Francisco-Bay Area, ACT Test Prep in Los Angeles, ISEE Test Prep in Philadelphia, LSAT Test Prep in San Diego, SSAT Test Prep in San Diego, GMAT Test Prep in Dallas Fort Worth, ACT Test Prep in New York City, ACT Test Prep in Miami, MCAT Test Prep in Chicago, GMAT Test Prep in Chicago

DMCA Complaint

If you believe that content available by means of the Website (as defined in our Terms of Service) infringes one or more of your copyrights, please notify us by providing a written notice (“Infringement Notice”) containing the information described below to the designated agent listed below. If Varsity Tutors takes action in response to an Infringement Notice, it will make a good faith attempt to contact the party that made such content available by means of the most recent email address, if any, provided by such party to Varsity Tutors.

Your Infringement Notice may be forwarded to the party that made the content available or to third parties such as ChillingEffects.org.

Please be advised that you will be liable for damages (including costs and attorneys’ fees) if you materially misrepresent that a product or activity is infringing your copyrights. Thus, if you are not sure content located on or linked-to by the Website infringes your copyright, you should consider first contacting an attorney.

Please follow these steps to file a notice:

You must include the following:

A physical or electronic signature of the copyright owner or a person authorized to act on their behalf; An identification of the copyright claimed to have been infringed; A description of the nature and exact location of the content that you claim to infringe your copyright, in \ sufficient detail to permit Varsity Tutors to find and positively identify that content; for example we require a link to the specific question (not just the name of the question) that contains the content and a description of which specific portion of the question – an image, a link, the text, etc – your complaint refers to; Your name, address, telephone number and email address; and A statement by you: (a) that you believe in good faith that the use of the content that you claim to infringe your copyright is not authorized by law, or by the copyright owner or such owner’s agent; (b) that all of the information contained in your Infringement Notice is accurate, and (c) under penalty of perjury, that you are either the copyright owner or a person authorized to act on their behalf.

Send your complaint to our designated agent at:

Charles Cohn Varsity Tutors LLC
101 S. Hanley Rd, Suite 300
St. Louis, MO 63105

Or fill out the form below:

Do not fill in this field

Contact Information

* Full legal name

Company name

* Phone number

* Email address

Address

* Address1

Address2

* City

* State

* Zipcode

* Country

Complaint Details

* URL of copyrighted work (where your original material is located)

* Please describe the copyrighted work so that it may be easily identified

I am the owner, or an agent authorized to act on behalf of the owner of an exclusive right that is allegedly infringed.

I have a good faith belief that the use of the material in the manner complained of is not authorized by the copyright owner, its agent, or the law.

This notification is accurate.

I acknowledge that there may be adverse legal consequences for making false or bad faith allegations of copyright infringement by using this process.

* Signature (your digital signature is legally binding)

HIGH SCHOOL

GRADUATE SCHOOL

K-8

Search 50+ Tests

math tutoring

science tutoring

foreign languages

elementary tutoring

other

Search 350+ Subjects

AP Physics 1 : Motion in Two Dimensions

Study concepts, example questions & explanations for AP Physics 1

All AP Physics 1 Resources

Example Questions

Example Question #21 : Motion In Two Dimensions

Example Question #351 : Newtonian Mechanics

Example Question #21 : Motion In Two Dimensions

Example Question #21 : Motion In Two Dimensions

Example Question #111 : Linear Motion And Momentum

Example Question #111 : Linear Motion And Momentum

Example Question #352 : Newtonian Mechanics

Example Question #22 : Motion In Two Dimensions

Example Question #22 : Motion In Two Dimensions

Example Question #353 : Newtonian Mechanics

All AP Physics 1 Resources

Report an issue with this question

DMCA Complaint

Contact Information

Address

Complaint Details

Email address:
Your name:
Feedback: