### Unit 3: Kinematics in Two Dimensions

Most motions in nature follow curved paths rather than straight lines. Motion along a curved path on a flat surface or a plane is two-dimensional and thus described by two-dimensional kinematics. Two-dimensional kinematics is a simple extension of the one-dimensional kinematics covered in the previous unit. This simple extension will allow us to apply physics to many more situations, and it will also yield unexpected insights about nature.

**Completing this unit should take you approximately 16 hours.**

### 3.1: Kinematics in Two Dimensions

Read section 3.1 of "Chapter 3: Two-Dimensional Kinematics" (pages 85 to 88).

### 3.2: Vector Addition and Subtraction

Read this material carefully before viewing the Khan Academy lecture sequence below.

Watch this lecture series, pausing to take notes, before moving on to the reading below. Don't worry if it seems intimidating. We will review the dot and cross products at a more appropriate level later when they are needed for this course.

Click the play button to start the animation. Observe that the physical result (the ball falls at the sailor's feet) is independent of our position while we watch the event as well as our movement relative to the event we are observing. This illustrates the same principle as the cart and golf ball in the previous lecture.

Click the play button to start the animation.

Click the play button to start the animation.

Click the play button to start the animation.

Click the play button to start the animation. In this animation, you will vary the x and y components of a vector and observe the resulting vector and its magnitude.

### 3.3: Constant Acceleration Motion

Read sections 3.2 and 3.3 of "Chapter 3: Two-Dimensional Kinematics" (pages 88 to 100). Look over the corresponding conceptual questions on pages 116 and 117 to test your understanding of the sections.

Try solving these practice problems. If you attempted this problem set prior to

**February 24, 2017,**and you would like to review your attempt, you may do so here.Work on solving problems 1, 2, and 3 from SAC106 and problems 1 through 4 from SAC109A. The solutions are available, but make a serious attempt to solve the problems before looking at the solutions.

### 3.4: Projectile Motion

Read sections 3.4 and 3.5 of "Chapter 3: Two-Dimensional Kinematics" (pages 101 to 113). Look over the corresponding conceptual questions on page 117 to test your understanding of the sections.

Try solving these practice problems.

Click the play button to start the animation. View the 3 frames to understand the relative roles of position, velocity, and acceleration in projectile motion.

Click the play button to start the animation. Vary the controls to create at least 10 different situations. Analyze the results for a few of them to assure yourself that the displayed trajectories accurately represent the projectile's motion under the influence of gravity. Do you find the gravitational acceleration to be 9.8 m/s

^{2}?Click the play button to start the animation.

Vary the initial conditions to demonstrate that the vertical acceleration and the horizontal motion are independent of each other. This is a simple version of a common projectile problem.

Work on solving problems 1, 2, 3, and 4 from SAC10. The solutions are available, but make a serious attempt to solve the problems before looking at the solutions.

### Unit 3 Assessment

Please take this assessment to check your understanding of the materials presented in this unit.

**Notes:****There is no minimum required score to pass this assessment, and your score on this assessment**__will not__factor into your overall course grade.**This assessment is designed to prepare you for the Final Exam that will determine your course grade. Upon submission of your assessment you will be provided with the correct answers and/or other feedback meant to help in your understanding of the topics being assessed.****You may attempt this assessment as many times as needed, whenever you would like.**