This graphic shows a typical setup for a projectile motion problem. Figure 1 shows a diagram of the setup for this experiment. Fortunately, we can take the same set of equations and apply them to the x and y directions independently - motion in the "y" direction does not affect motion on the "x" direction, and vice versa. However, these equations are only for one dimension, and the catapult-launched ball in this experiment is going to be moving in two dimensions - x and y. For example, if you are running at an initial velocity of 3 m/s and accelerating at a rate of 1 m/s², you can use Equation 2 to calculate that your final velocity will be 5 m/s after a time (t = 2) seconds passed by: Given certain information about an object at one time, these equations let you calculate what is happening at another time. Stands for elapsed time, usually expressed in seconds (s). Usually expressed in meters (m) velocity, usually expressed in meters per second (m/s) andĪcceleration, usually expressed in meters per second squared (m/s²). The variables d, v, and a stand for distance, In these equations, the subscripts i and f stand for initial andįinal, respectively. ( Note: Hover over the equations in this Introduction with your cursor to view enlarged formulas.)Įquation 1: Įquation 2: Įquation 3: Įquation 4: These equations rely on the assumption that we can ignore air resistance - otherwise, the acceleration would change over time, and not be constant.
For this project we will use simplified constant acceleration equations. A more advanced understanding of projectile motion involves calculus and factors like air resistance. Understanding projectile motion requires an understanding of position (the location of the ball, or projectile), velocity (how fast the ball is moving), and acceleration (how fast the velocity changes). For this project, we are only concerned with projectiles. Kinematics (the study of motion) broadly includes things like pulleys, linkages, and gears. You may hear "projectile motion" used interchangeably with the word kinematics, depending on the textbook, website, or teacher. Projectile motion refers to the method used for calculating the trajectory of a projectile (which can be pretty much any physical object - a rock, a ball, etc.) as it moves through the air. Predicting the trajectory of a ball launched from the catapult requires an understanding of two fundamental physics concepts: projectile motion and conservation of energy.
Part of the scientific process involves figuring out what those factors are so you can make better predictions next time. There are many real-world factors that can be difficult to account for in predictions. If the results match, you can conclude that your predictions and the assumptions you used to make them were valid under the circumstances of the test. You can also use physics to predict the trajectory of the ball, and then compare this predicted trajectory to the one you measure from video recordings. Well, it is a lot more fun if you actually get to use a catapult instead of just doing the calculations! In this science project, you will use a catapult to launch ping-pong balls and use a video camera to film their trajectory, or path, as they fly through the air. You have probably seen figures in your physics textbook that show a catapult launching a projectile and then equations that calculate the resulting trajectory.
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