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# Chapter 3: Two-Dimensional Kinematics

In this chapter we generalize the study of motion in one dimension to the motion of objects in two dimensions. In doing so we discuss two of the most important forms of two-dimensional motion, projectile motion and circular motion.

# Table of Contents

## Illustrations

- Illustration 3.1: Vector Decomposition.
- Illustration 3.2: Motion on an Incline.
- Illustration 3.3: The Direction of Velocity and Acceleration Vectors.
- Illustration 3.4: Projectile Motion.
- Illustration 3.5: Uniform Circular Motion and Acceleration.
- Illustration 3.6: Circular and Noncircular Motion.

## Explorations

- Exploration 3.1: Addition of Displacement Vectors.
- Exploration 3.2: Run the Gauntlet, Controlling x, v, and a.
- Exploration 3.3: Acceleration of a Golf Ball That Rims the Hole.
- Exploration 3.4: Space Probe with Constant Acceleration.
- Exploration 3.5: Uphill and Downhill Projectile Motion.
- Exploration 3.6: Uniform Circular Motion.

## Problems

- Problem 3.1: Rank the 5 vectors.
- Problem 3.2: Two vectors are shown on the coordinate grid.
- Problem 3.3: Rank the motion diagrams.
- Problem 3.4: A bowling ball is lifted from rest onto a shelf.
- Problem 3.5: A helicopter takes off.
- Problem 3.6: A hot-air balloon takes off.
- Problem 3.7: A projectile is launched.
- Problem 3.8: Shoot the apple from the tree.
- Problem 3.9: Projectile motion problem.
- Problem 3.10: Aim the projectile to hit the moving Lamborghini.
- Problem 3.11: A red ball slides off a table.
- Problem 3.12: A basketball bounces on the floor.
- Problem 3.13: A putted golf ball rolls in a straight line toward the hole.
- Problem 3.14: A space probe travels with a constant acceleration.
- Problem 3.15: An object travels along a circular path.
- Problem 3.16: Rotating square.
- Problem 3.17: Uniform circular motion of a wheel.