![]() In other cases we may choose a different set of axes. It is not required that we use this choice of axes it is simply convenient in the case of gravitational acceleration. (This choice of axes is the most sensible because acceleration resulting from gravity is vertical thus, there is 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. As a result, the time taken for the ball to reach the batter is only about 5 longer than in a vacuum, and the actual trajectory is also very similar.2 In. It is derived using the kinematics equations: a x 0 v x v 0x x v 0xt a y g v y v 0y gt y v 0yt 1 2 gt2 where v 0x v 0 cos v 0y v 0 sin Suppose a projectile is thrown from the ground level, then the range is the distance between the launch point and the landing point, where the projectile hits the ground. ![]() 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. Since this is motion in 2 dimensions, we will want to find the horizontal and vertical components of the initial velocity v 0x (30m/s)cos(20°) 28.2m/s v 0y (30m/s)sin(20°) 10.3m/s Sample Problem 1 A baseball is thrown with an initial speed of 30 m/s, at an angle of 20°above the horizontal. 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. Figure 4.12 (a) We analyze two-dimensional projectile motion by breaking it into two independent one-dimensional motions along the vertical and horizontal axes. Some examples include meteors as they enter Earth’s atmosphere, fireworks, and the motion of any ball in sports. Thus, any projectile that has an initial vertical velocity of 21.2 m/s and lands 10.0 m above its starting altitude spends 3.79 s in the air. The applications of projectile motion in physics and engineering are numerous. As mentioned earlier, the time for projectile motion is determined completely by the vertical motion. 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. ![]() By the end of this section, you will be able to: ![]()
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