In this section, we consider two-dimensional projectile motion, such as that of a football or other object for which air resistance is negligible. The motion of falling objects, as covered in Problem-Solving Basics for One-Dimensional Kinematics, is a simple one-dimensional type of projectile motion in which there is no horizontal movement. The object is called a projectile, and its path is called its trajectory. Projectile motion is the motion of an object thrown or projected into the air, subject to only the acceleration of gravity. 3.A.1.3 The student is able to analyze experimental data describing the motion of an object and is able to express the results of the analysis using narrative, mathematical, and graphical representations.3.A.1.1 The student is able to express the motion of an object using narrative, mathematical, and graphical representations.The information presented in this section supports the following AP® learning objectives:

Apply the principle of independence of motion to solve projectile motion problems.Determine the location and velocity of a projectile at different points in its trajectory.Identify and explain the properties of a projectile, such as acceleration due to gravity, range, maximum height, and trajectory.The trajectory of a rock ejected from the Kilauea volcano.By the end of this section, you will be able to: (b) What are the magnitude and direction of the rock’s velocity at impact? Figure 4. (a) Calculate the time it takes the rock to follow this path. The rock strikes the side of the volcano at an altitude 20.0 m lower than its starting point. Figure 1 illustrates the notation for displacement, where extbfabove the horizontal, as shown in Figure 4. (This choice of axes is the most sensible, because acceleration due to gravity is vertical-thus, there will be no acceleration along the horizontal axis when air resistance is negligible.) As is customary, we call the horizontal axis the x-axis and the vertical axis the y-axis. The key to analyzing two-dimensional projectile motion is to break it into two motions, one along the horizontal axis and the other along the vertical. This fact was discussed in Chapter 3.1 Kinematics in Two Dimensions: An Introduction, where vertical and horizontal motions were seen to be independent. The most important fact to remember here is that motions along perpendicular axes are independent and thus can be analyzed separately. The motion of falling objects, as covered in Chapter 2.6 Problem-Solving Basics for One-Dimensional Kinematics, is a simple one-dimensional type of projectile motion in which there is no horizontal movement. Projectile motion is the motionof an object thrown or projected into the air, subject to only the acceleration of gravity.

Angular projectile motion problems