### 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.**

Upon successful completion of this unit, the student will be able to:

- add and subtract vectors;
- determine the components of a vector given its magnitude and direction, and determine the magnitude and direction of a vector given its components; and
- separately analyze the horizontal and vertical motions in projectile problems.

### 3.1: Kinematics in Two Dimensions

Read section 3.1 of "Chapter 3: Two-Dimensional Kinematics".

### 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.

### 3.3: Constant Acceleration Motion

Read sections 3.2 and 3.3 of "Chapter 3: Two-Dimensional Kinematics". Look over the conceptual questions at the end of each section to test your understanding.

Try solving these practice problems.

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". Look over the conceptual questions in each section to test your understanding.

Try solving these practice problems.

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

Take this assessment to see how well you understood this unit.

- This assessment
**does not count towards your grade**. It is just for practice! - You will see the correct answers when you submit your answers. Use this to help you study for the final exam!
- You can take this assessment as many times as you want, whenever you want.

- This assessment