https://youtu.be/FXKgXxRUSrc
PHYS 1101: Lecture Nine, Part Seven
The next step is to have you do an example, and to follow the same problem solving steps, and there are some quiz questions associated with this as you work through this example. Your problem is Romeo trying to get Juliet’s attention. He’s chucking pebbles up to her window, and he wants the pebbles to hit the window with only a horizontal component of the velocity.
Hint number 1: That means a velocity that’s just like that, dead horizontal. When he lets go of the pebble, the pebble itself is 9 meters horizontally from the wall and 8 meters below the window. How fast were the pebbles going when they hit her window?
Okay, step 1: Be sure… start to sketch this and have a scenario of it. Decide what object are you focused on? What’s the start? What’s the end? The object is not Romeo, it’s not Juliet, it’s the pebble, the rock. The rock is a projectile once he lets go of it and just before it hits the window. During that time interval nothing is touching it. It’s a projectile. That’s the duration of our problem.
So let me help you out and just sketch. The pebble starts out here, makes an arc path up to her window, and the end of the problem would be something like that. To that sketch add more information, read this carefully, and sketch where the… what corresponds to 8 meters? What’s 9 meters? Add the initial velocity vector and the final vector to this. What’s the acceleration vector for this projectile, this pebble, after it leaves his hand and before it hits the window? After you’ve done as much sketching there as you can and you think you’ve got a good visual of the problem, you’re ready for step 2.
Let’s pick the standard axis definitions plus y up, plus x to the right, and I’ve provided you with a large x and y axis here, so translate the drawing information you have above onto this coordinate system and then you need to go through and answer these quiz questions, 8 through 13.
All these ask you to do is to envision and decide on the proper direction for the three major vectors for this problem, for any problem: Initial velocity, final velocity, and the acceleration vector. Once you have a feeling for what sign to expect and what direction these vectors should be pointing, go back to the information that you have and see if there’s any vectors that you can apply trigonometry to, to try to get values for components. So this would be before you’re applying any of the equations to it. This is just given the initial problem information, how many components can you figure out?
Then do step 4, problem solving step. Make a list of the knowns that you have. I highly recommend, draw yourself on the left an x and a line, and go through all your x variables. There should be five. Wait, let me see. Initial position, final position, initial velocity component, final velocity component, acceleration component. 1, 2, 3, 4, 5, yup, 5.
For y do the same thing. There’s five of those. Y 0, whoops, final y coordinate, initial y component of velocity, final y component of velocity, Ay, and then in between these I have the time variable, starting the clock at 0, but then what’s the final time? Do I know that value? And leave it blank for you.
Then you’re ready for Question 14. After you’ve filled in those variables, at this point without further calculation, how many variables do you have a value for? So go through them, count them. How many do you know? If one of those variables is 0, like t0, count it. So, here’s 1 for you. You know the answer is greater than 1. I’ll just tell you it’s not 1. It’s definitely greater than 1.
Question 15, then, is having you follow through and determine the answer to this problem. How fast are the pebbles going when they hit her window? Let me point out how fast is going to be the speed of the final velocity vector. That final velocity vector looks like this because it told us that those pebbles are hitting the window horizontally. There’s no Vy component at the end of our problem. I only have a horizontal component to that velocity.
What’s the magnitude of this? What’s the magnitude of Vx? This is step 5 that you’re doing. You’re going to look at your list of knowns, look at our equations, and do your best to answer that question.
Let me remind you again by blacking out for a projectile because Ax is 0, that equation goes away, it doesn’t give us anything useful to work with. Neither does the last one, and in fact equation 2 is the only equation for x that we have.
Let me suggest that with this problem, like many of these projectile problems, you may have to solve for the time to connect horizontal motion to the vertical motion to be able to solve the problem.
I’m finishing off this lecture with a few questions that I’ve taken as samples of MCAT questions. I found a source of these and so on occasion I’ll sprinkle these through our lectures for those of you that are headed to medical school.
Question 16 is which trajectory describes a ball rolling down a curved ramp that ends at point P. So there’s a little upward scoop, it looks like, ever so slight at point P. This is point P. What trajectory does the ball take once it leaves that point? And it’s rolling down a curved ramp so just to help you out that of course has to mean it’s a projectile once it leaves the ramp, acceleration is straight down.
Question 17, you have a cannon that’s placed on the flat car of a train. Here’s my train. Here’s my cannon. The cannon fires a ball vertically upward, and it gives the ball an initial upward velocity or speed of 10 meters per second, but at the same time this cart or the train, I’m sorry, is moving to the right at 5 meters per second. This is a lot like that bulldozer movie that I showed you where you really can see that the motion that your eye sees for the ball or this object, the bulldozer, is a combination of the vertical and the horizontal motion. So, you will want to think about how the magnitudes of these two velocity components, these two speeds compare.
The last question is a little tricky, and I’m going to treat this as a bonus question, and I’m going to make the stakes nice and high because I really want you to think about this and put a lot of these concepts together for a projectile. If 70 percent of you get this right, I’ll give everybody plus 8, otherwise I’ll give everybody plus 3 for just taking a shot at it.
Now, go pause the lecture, read it carefully… oh sorry let me give you choices here. This is A, B, C, and D, and make your choice. Just realized I forgot to give you the choices for the above ones too. I guess these we can call choice A, B, C, and D. All right that brings us to the end of Lecture 9.