![]() 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. We discussed this fact in Displacement and Velocity Vectors, where we saw that vertical and horizontal motions are independent. The most important fact to remember here is that motions along perpendicular axes are independent and thus can be analyzed separately. In this section, we consider two-dimensional projectile motion, and our treatment neglects the effects of air resistance. The motion of falling objects as discussed in Motion Along a Straight Line is a simple one-dimensional type of projectile motion in which there is no horizontal movement. Such objects are called projectiles and their path is called a trajectory. ![]() Some examples include meteors as they enter Earth’s atmosphere, fireworks, and the motion of any ball in sports. The applications of projectile motion in physics and engineering are numerous. Projectile motion is the motion of an object thrown or projected into the air, subject only to acceleration as a result of gravity. Calculate the trajectory of a projectile.Find the time of flight and impact velocity of a projectile that lands at a different height from that of launch.Calculate the range, time of flight, and maximum height of a projectile that is launched and impacts a flat, horizontal surface.Use one-dimensional motion in perpendicular directions to analyze projectile motion.Let us consider projectile range further.įigure 3.40 Trajectories of projectiles on level ground.By the end of this section, you will be able to: However, investigating the range of projectiles can shed light on other interesting phenomena, such as the orbits of satellites around the Earth. Galileo and many others were interested in the range of projectiles primarily for military purposes-such as aiming cannons. The components of acceleration are then very simple:Ī y = – g = – 9.80 m /s 2 a y = – g = – 9.80 m /s 2 size 12 traveled by a projectile. We will assume all forces except gravity (such as air resistance and friction, for example) are negligible. We must find their components along the x- and y-axes, too. ![]() Of course, to describe motion we must deal with velocity and acceleration, as well as with displacement. However, to simplify the notation, we will simply represent the component vectors as x x and y y.) If we continued this format, we would call displacement s s with components s x s x and s y s y. (Note that in the last section we used the notation A A to represent a vector with components A x A x and A y A y. The magnitudes of these vectors are s, x, and y. Figure 3.36 illustrates the notation for displacement, where s s is defined to be the total displacement and x x and y y are its components along the horizontal and vertical axes, respectively. (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 Kinematics in Two Dimensions: An Introduction, where vertical and horizontal motions were seen to be independent. 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.
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