https://youtu.be/tb61xAbCBNE
PHYS 1101: Lecture Eight, Part Four
So here are the steps. As we look through them and then we are going to practice applying them to a problem. You will notice that they are very similar to the steps for the 1D problems, there’s only a few more levels of complication.
First you will notice, of course, that our equations instead of just being three are now six. A set of three for x, a set of three for y. Our number of variables has gone up. It’s still time, position, velocity that we need at the start, and at the end, but now for position and velocity we are going to have to think of the components say the final position, and the final velocity and then acceleration, it’s going to have components. So that extends our total number of unique variables that describe two dimensional motion from 7 to 12. 12 if you count t sub 0 being set to 0. Okay that’s the first difference.
The next difference to emphasize is, I’ve added a new step here, number 3 which is after you have done some initial visualization you’ve drawn your axes and your origin and you’ve done something to sketch and have a visual of what this trajectory is. You’ve thought through some of your initial variables. Do some initial trigonometry to calculate as many components as you can. For example you may be told that the initial speed is 3 meters per second at 30 degrees from the horizontal. 3 meters per second is hypotenuse. That’s the magnitude of the vector that has this x and this y component. Do your trigonometry. Calculate the values for these two components. Do as many of those as you can in step 3.
Step 4. It’s the same idea, we are making a list of the variables for which we have a value for and then from the list of twelve we have to pick, or focus on, the variables that are going to allow us to get an answer for this question or this problem.
Then Step 5, it’s the same idea of picking your equations, algebra-ing your way to a solution, and then paying attention to, once you get a value for your variables, carefully go back and revisit what the problem specifically asks. Because often what they are asking for is not a component value, which are the variables that you work with, but rather the hypotenuse or the resultant vector value. They may want an initial speed, a final speed or the magnitude of acceleration.
Let me point out one more thing that will help with the strategy as you start working with the equations. I’ve emphasized that the horizontal vectors impact each other and only the vertical vectors impact other vertical vectors. But the horizontal and the vertical part to the motion is occurring at the same time. So a key variable that defines that to be true is the time, the variable t. In this set of equations is the same t, in this set. That will be a trick to solving many of these problems. You’ll find that you’ll work with one set of equations, say horizontal information ultimately to get your answer, but in order to arrive at a final say, answer for the final horizontal position you’ll need to get the time. There won’t be enough information about the horizontal motion to do that but if you go over and think about the vertical motion of what’s happened in the same problem there is enough information there to solve for the time. So time is often the secret variable that you need to go after in the middle of a problem in order to work to the end solution.
A copy of these problem solving steps is in your Equation and Useful Information link. They are now the fourth page added at that link. That’s that green chalkboard link you have on your homepage.