https://youtu.be/4eLTie3i-8U
PHYS 1101: Lecture Nine, Part Two
In the previous lecture we just went through our problem solving steps, and I worked an example for you and then had you walk through solving a two dimensional trajectory problem. I can best summarize the steps that we have to go through to do that in this fashion of having three main components.
When we read these problems in the real world, we’re going to have a scope to a problem, a beginning, and an end. And during that time interval the problem has to have a constant acceleration. This delta-v vector has to be the same direction in length from start to finish.
What happens is I’ll start off with some initial speed at an initial angle that defines an initial velocity, v0, and then the clock ticks on. That velocity changes because of the acceleration to leave me with the final velocity, a final speed, and a final direction. That’s what your eye’s drawn to. That’s what you are going to read in the problem. It’s the real world description.
In order to do the mathematics to solve the physics behind the problem, we need to take these vectors, and we need to strip out their components, so to speak. We need to pull out all of the x components of those vectors and the y components of those three vectors. The beauty of that is these components then we can treat as one dimensional motion as the components. The parameters are important for one dimensional motion.
Being in one dimension now the scalar components can have a sign associated with them that keeps track of the direction of the vectors. The interesting comparison or the connection between the horizontal and the vertical parts is that the time variable is the same for both. The horizontal motion is occurring at the same time as the vertical motion.
This was the same case back when we did one dimensional problems where we may have had two objects undergoing motion at the same time where time was the same variable in those two sets of equations.
So we do our mathematics here, these two one dimensional pictures, noting the time is a common variable. We set our clock to 0 at the initial instant, and that final time, the duration of the problem, that t shows up in these equations and in these equations. Once we work with these equations and we’ve chosen, we’ve focused on specific variables here that we have to solve for, those variables then we have to use to answer the real problem that was posed.
Often that real problem has us tying the mathematics back to the real world or translating the mathematics back into what’s happening. It may ask us for an initial speed, the initial magnitude of this velocity or a final speed or the magnitude of the acceleration. These are hypotenuse pieces of information.
For example, to get this initial speed, I have to use the Pythagorean theorem where this and this are the two sides of a right triangle. And this, the speed, is the hypotenuse.
Here’s our reading quiz for this section. We just had to read Section 3.3 on projectile motion for this lecture. Question 3: With the standard axis definition positive y being up and positive x to the right, when we’re working with projectile motion what’s the value of Ax? For all projectiles this will be true. Is it A) positive, B) negative, C) 0, or D) does it depend on some details of that particular problem?
Question 4: With the same standard axis definitions in projectile motion, the value of Ay is A) positive, B) negative, C) 0, or D) does it depend on the details?