mr.p: Good morning. Today we are going to begin learning about projectile motion. Here we go. Bo: Hey, guys. Billy: Hey, Bo. Bobby: Hi, Bo. ♫ (lyrics) Flipping Physics ♫ mr.p: Before today, we have analyzed many different examples of motion. Objects moving with a constant velocity, objects with a constant acceleration, both positive and negative, including a constant negative acceleration where the object was speeding up. We analyzed uniformly accelerated motion with two different accelerations. We analyzed free-fall acceleration. We compared the motion of a ball that was thrown upward to that of a ball that was dropped. We analyzed what happened when we dropped objects with different masses from the same height. We even used stop motion photography to graph the position as a function of time of a dropped ball. Every one of those was an example of linear motion. Today, we are going to go beyond linear motion to (dramatic music) projectile motion. (dramatic music) (laughing) Perfect! mr.p: Welcome to Projectile Motion. All: Projectile motion. mr.p: When an object is flying through the vacuum that you can breath in at least two dimensions, it is moving in what we call projectile motion. Billy: Mr. P., do we get to do more than two dimensions? mr.p: No. Two dimensions, the x and y directions, are enough for this class. Billy: That's a bummer. Bo: What is the vacuum you can breathe? Bobby: Remember, that's just the air with no air resistance. Bo: Oh, yeah. mr.p: Here is my basic strategy for solving a projectile motion problem. You need to split your known variables into what you know in the x direction and what you know in the y direction. "Why?" Billy and Bo: Why? mr.p: you might ask. It's because the equations of motion, the equations that describe the motions of the object in projectile motion are different in the x direction and the y direction. Billy, tell me, as the object is flying through the vacuum that you can breathe in two directions is it touching anything? Billy: No, it's not touching anything. mr.p: Then, Bobby, tell me, is the object freely falling? Bobby: Yes, it's in free-fall. mr.p: Then, Bo, tell me what we know about an object in free-fall. Bo: It has an acceleration of 9.81. Bobby: Don't forget the negative. Bo: Negative 9.81. mr.p: Bo, dimensions please. Bo: It has an acceleration of negative 9.81 meters per second squared. Billy: In the y direction. Bo: In the y direction. mr.p: So an object in projectile motion in the y direction is in free-fall, and we know the acceleration in the y direction is going to be equal to negative g, where on Earth g is a positive 9.81 meters per second squared. In other words, in the y direction the acceleration is equal to negative 9.81 meters per second squared. Therefore, Billy, what equations can we use in the y direction for an object in projectile motion? Billy: Oh yeah. Because the acceleration is a constant number, we can use the UAM, or uniformly accelerated motion equations. mr.p: Therefore, when an object is in projectile motion in the y direction, we can use the UAM equations, or uniformly accelerated motion equations, and we already know the acceleration, it's negative 9.81 meters per second squared. Now, let's take a look at the x direction. When I drop this ball, does the ball accelerate to the left or to the right? Bo: What? mr.p: Is the ball accelerating to the left or to the right? Bobby: Uh, neither. It moves straight down. mr.p: Correct. The ball doesn't move to the left or to the right because nothing's pushing it to the left or to the right, so there's no acceleration to the left or to the right, which means it is moving at a constant velocity in the x direction. With the dropped ball, that just means that the velocity in the x direction is a constant value of zero. When an object is in projectile motion, that just means that the velocity in the x direction will maintain a constant non-zero value. And remember the equation for velocity. The velocity in the x direction equals the displacement over the change in time. Now, again, notice that the equations of motion are different in the x and y directions. Bo, please tell me what are the possible variables in the x direction. Bo: Well, there's only one equation, so velocity in the x direction, change in position, and change in time. mr.p: Notice, because there's one equation and three variables, you need to know two of the variables in order to figure out the other one. Now, let's look at the y direction. Bobby, please list all the possible UAM variables. Bobby: Uh, let's see. Velocity final, velocity initial, acceleration, change in time, and displacement. mr.p: Class, there are how many UAM variables? All: Five. mr.p: And how many UAM equations? All: Four. mr.p: And if you know how many of the UAM variables? All: Three. mr.p: You can figure out the other All: two, mr.p: which leaves you with one All: happy physics student. Billy: Yeah. mr.p: So in the y direction, you need to know three variables, and in the x direction you only need to know two in order to solve the equations. But what are we going to be solving for? Billy, please tell me which one of the UAM variables is a scalar? Billy: The only that's a scalar is change in time. mr.p: In other words, if you solve for the change in time in one direction, you can then apply that to the other direction because the change in time is a scalar and is independent of direction. In other words, the change in time is almost always what you're going to be solving for in a projectile motion problem, and then applying it to the other direction. Let's do a quick review. When you have a projectile motion problem you need to list what you know in the x direction and the y direction separately. In the y direction it's an object in free-fall, therefore the acceleration in y direction equals negative 9.81 meters per second squared, therefore, you can use the UAM equations and you need to know three variables in order to solve in the y direction. In the x direction, there is no acceleration, so the object's moving at a constant velocity, therefore, you can use the equation for constant velocity and you only need to know two variables in the x direction to solve the equation. And, the change in time is a scalar, therefore, independent of direction, and that is generally what you're going to solve for in projectile motion problems. Thank you very much for learning with me today. I enjoyed learning with you.