So sometimes your vectors are not parallel and when they are not parallel, you cannot just add and subtract their magnitudes. For example, you can look at this drawing here. We have two vectors, they are not parallel.
So what to do? Okay, so there are a few methods to solve this problem. I'm going to start with the first one, which is scaled drawing. In this video, we are going to look at a pass here paper from May-June 18, paper 2-1, question 1c.
You can look for it in your handout or where you normally get your pass here questions. We're going to study how to find the resultant velocity. of an aircraft. So let's read the question using the scale drawing method.
Okay so we have an aircraft traveling in wind, flying. Okay and figure 1.2 which is this drawing shows the velocities of the aircraft in still air and for the wind. Okay so right now this aircraft is just flying. This one is in still air.
So if you read the question right it says here that the velocity of the aircraft in still air is 95 meter per second so this is 95 right and you are going to look at this side it says that it is headed to the west so this aircraft is pointing to the west so if you are a little bit not sure you can always draw something like that on the side north north pole whenever you look at the world map is here Okay, south is down here. East is where Malaysia is, you know, Southeast Asia. Our country is somewhere here on the map, represent.
Okay, and west is here. So when you look at this, this is pointing to the west. Okay, and you see the second vector, which is this wind velocity is 28. This is 28 meter per second, 65 degrees south of. east. So this question is very nice.
They draw for you already where the resultant, I mean where is the 65 degrees south of east is. But in case they don't draw, here is how you can see where 65 south of east look like. Okay so number one, you can draw the crosshair here okay and when they say 65 south of east, it's pointing towards. So it's here is pointing towards so you almost draw at the end.
just like for example for this aircraft velocity you will draw here and the aircraft velocity is pointing in this direction okay so it's pointing to the west so right now what we'll do you can see this is south this is east so it's 65 degrees from east or south rotate to the south so 65 degrees south of east. So you start at east, start here, and then you rotate 65 degrees towards the south direction. Okay? But most of the time, good news is we will draw for you.
Okay? So once we get that out of the way, we now want to find the resultant velocity here. Part 1. On figure 1.2, draw an arrow navel r in the direction of the resultant velocity.
of the aircraft and part two determine the magnitude of this resultant velocity okay so we are going to stare at the vector diagram a bit and a common mistake is you see a triangle then you feel like oh i should draw like that no move this one is no move because if you look at the arrow i follow the direction of wind velocity so let me change color a bit Let's say I follow the direction of wind velocity. Okay. And let's say this wind velocity is going in this direction.
Okay, roughly. And then it goes in this direction too. But how does it fit in the blue arrow?
So obviously, not like that. Okay. So you cannot draw this because this doesn't make sense. Your arrows must follow one after the other.
So in this case, I will just silently rub this off. And what I'll do during the exam, because this is paper too, so this one is printed out for you, is I'll take my ruler, and I will measure the length of this wind balloon. So I don't have a ruler, but I'll measure the length.
So whatever this length is, I'm going to... copy and paste here as parallel as possible but if you just want to be extra careful then bring with you a protractor into the exam hall. Have a protractor with you. Okay, so let me highlight this one, change the color.
So this is your wind velocity and also your 28 meter per second. All right, so you measure the length, must be the same length. Okay, and then now you look at this, you can see, oh well, first I move to the west like this and then I move up like this.
Isn't it the same as us moving directly in this way? Yes, okay. So just imagine yourself walking the path, which is the easiest way to do that visualizing.
Okay, so I'm going to draw that resultant vector now. This one is blue color and I'll try to draw a bass arrow now. Okay, so it's going to look something like this. this so you should be able to draw an r that is roughly pointing in this direction okay and please label this arrow they ask you to label r you also label law so this one okay so you draw this you get one mark already teacher if not very accurate can i can't because it's just drawing so if you draw in that direction you will get the first mark But when it comes to magnitude, right now, if you actually measure using your ruler, then you can look for the magnitude. So if you print out the notes that I've given you, because you know I wanted to save you some printing cost, I shrink the page okay.
So when I shrink the page, I will shrink the scale as well. So to make you understand what is going on, I am going to copy the diagram into a piece of paper. and show you how it looks like when you draw this on your own.
Okay so I'm back. Alright so this is this little baby here is recording my hands. Alright and I'm going to try to draw this out on a piece of A4 paper. Okay so normally during the exam, not in COVID-19 time, they will print out paper for you.
You can print this out in the full size if you go and find the actual May-June 18 paper. Okay, and then you can actually measure the lengths to find out what scales they're using. But right now, let's say I don't have that.
So I'm just going to use the good old 1cm, because you can see the biggest number here is 95. This one here, 95. Okay, so I'm going to use the scale. Now we'll denote the scale large here. The scale here that I will use is 1cm is equivalent to, so scale equal.
1 cm is equivalent to 10 m per second. So in this case, it really is up to the drawing that you are given, and then you measure. So you will take your ruler and try to measure. Oh, you see here?
This one is 9.5. So if 9.5, and then I'll draw an arrow here to represent, this is 95 m per second. So 9.5 cm is equivalent to 95 meter per second. So then I divide by 10, 9.5 cm, 95. There. So now I'm going to draw my wind velocity.
Wind velocity is at some angle like this. Measured from this line is 65. Okay. This angle here measured from the line is 65. So to be able to measure out that angle, I have with me my trusty compass.
Protractor, sorry, protractor. And when you measure, right, you should always try to understand that the angle, the center of the angle is here. This part, this 65 here.
Okay, let me show you. The center of the angle is here. Meaning to say, the center of my compass should also be there. Because now I want to measure 65. okay so of course if let's say you want to measure 65 down here then i will rotate this one down here like that okay so align this blue color uh blue color line the original line to zero okay you align this one to zero and then if you want 65 what you will do is you will add the degree okay so you're gonna add like 10 20 so you can always just check 65 is here somewhere here so here to here is 65 kind of makes sense all right so always use that to double check okay then how okay so i'm gonna i'm gonna i'm gonna just uh mark out 65 65 is here and put a dot.
Okay, I don't care about the length. I just want the angle here, dot. So this means if I join any point between here, the center of the protractor, and here, I'll get 65 degrees from the line. All right, so this is for you if you don't know this.
I'm going to draw 2.8 cm. I'm just going to make sure my ruler is aligned here like that. Okay, align with the dot. so i make bigger so you can see i align like that okay so 2.8 so i'm going to draw okay i'm going to be a parallax error but i'll try my best 2.5 2.8 is somewhere here and i'm drawing the pen danger okay so i'll mark this one out for myself this is 65 degree and this wind speed is a wind speed of 28. meter per second.
So this diagram, assume this diagram is given to you in the exam, okay, and you measure the length of this or this to get the scale. So now what do you do is you measure out this 2.8 cm and then you extrapolate and transfer here, basically repeating what I did just now but on the actual paper. So if you want to be extra like accurate, a compass will help, okay, a protractor will help, or a compass.
So in this case, I want 65 degree on this side. Alternate angle. Okay. This side, if you look at the one node behind my head, this side will be 65. Okay.
Alternate angle. Here and here. So I'm going to mark that out.
65 would be... So we read the bottom scale. Obviously right? Okay we're going to read the bottom scale because it doesn't make sense that here to here is 125. Let me move a bit so you can see.
So it doesn't make sense that here to here is 125. So it should be 65. Read the bottom scale okay. So if you put it properly it should they should all align on somewhat of a straight line now. but of course again all this is parallax error because i can't put my eye here so yeah okay so again just try my best uh to align the lines and from here what i'll get for 2.8 2.8 is somewhere here so i can just continue this line one this dot okay so i shall do that well of course the protractor is also okay so this is 2.8 And I'm moving it up.
This one is here. Of course, you can erase this one if you use pencil. Same vector.
Vector can move around one. So if you want to find the resultant, the resultant will be to join from where you started here, move to the left, okay? And then go upwards. Start here, turn up. So...
I will join the starting point to the end point as accurate as possible using pencil if you follow the drawing method and then you double-headed arrow here label this one as R now I take the ruler and I try to measure the length so if I check on the length for me it looks like I don't know man I'm gonna put it here so you can let it lower the camera a bit so you can see a bit clearer then it'll be a bit awkward okay so i'll try my best to align here notice the uncertainty you take one reading here half a scale uncertainty where the zero is go here another uncertainty half a scale so i'm thinking this is around 11. i don't know maybe yours would be more accurate. You draw yours, okay, without the limitations of camera blocking your parallax error. So half a small scale, half a small scale, there are two uncertainties when you start measuring, when you end measuring, because of the two reading, the uncertainty is actually plus minus 1 mm.
So I think it's around 1 mm-ish. Okay so I'm gonna write that down. Okay so just make a note here that the resultant velocity, come over here a bit so you can see, resultant Velocity will be equal to 11.0 cm.
If you want to write it with uncertainty, then you will say 11.0 plus minus 0.1 cm. Okay, but this is theory paper so we can stick to 11.0 cm. Okay, but you're going to have to multiply this by the scale.
So the scale is 10 meter per second for every cm. So the cm and cm will cancel. and when they cancel what you will get is 110 meter per second which is the speed of the egg okay so if you want to include the uncertainty then you're going to have to times 10 the uncertainty also have to times 10 right so then let's say this is v oh wait this is r sorry this is r okay so if you want to find the uncertainty in r i'll just continue here okay uncertainty in r will be equal to plus minus 0.1 cm, multiplied by the scale, I'm just teaching this extra, it's not needed in the question. I repeat, not needed in the question, I'm just doing this extra.
Okay, in case they ask, how do you know they don't ask? Okay, so anyway, you can cancel these two, and your absolute uncertainty will be plus minus 1 meter per second. So if you want to write your final answer, you can say r plus minus uncertainty in r, being the resultant velocity, will be 110. plus minus one meter per second.
This is how you can write your final form. Of course, if yours is not 11, then you do something else. But your absolute uncertainty here must be correct. So just a note here, this absolute uncertainty, this 0.1 is half the smallest reading times two.
So it's the smallest reading. Because when you put the ruler here and you measure the length of the red line, Here got uncertainty leo. Here another uncertainty. Half a scale, half a scale, one. Smallest reading okay.
Not the same as chemistry for those of you who do chemistry. Okay so done already oh. So this means right during the exam if you actually, because this blue thing is drawn for you, down here draw for you already.
What you need to do is to copy paste the arrow and put here and then join and then take your ruler to measure the length and to find the scale. the scale of this black line first and then to measure this length to find r. I think it's okay la.
I think you already started ma. You have to draw r to get one mark one. So if you draw r, you get one mark. Okay, if your scale drawing is labeled correctly and then you measure this, you get one mark. Okay, final answer is one mark.
So that means you are already halfway there. Scale drawing is workable but as you can see it is full of uncertainty, right? And the mark scheme allowed answer is actually quite generous. They will allow 108 to 112 meter per second. Okay, so it's a quite large range if I do say so myself.
Okay, so first method done. You draw a triangle correctly, please label everything. You draw the R correctly, you get one mark.
the rest of the triangle properly built should be there if not one mark can be deducted okay so the triangle drawing is one mark then uh you show all this calculation is actually the same mark my bad this one is the same mark okay i will scan this and put in the notes for you but yeah that's the whole idea so skill drawing when you draw this because you already did this mark so it's just a little bit of step to add on but some of you who are like teacher this this Range, very big leh. I like accurate answer. I want to be more precise.
Okay, okay, I hear you. You want to decrease your percentage uncertainty. You don't like this large range, I get it.
So another method is to use solution of triangles. Okay, so some of you who do AdMass, you're like, Teacher, I know the length of this blue line. I can calculate using equation. Okay, so the second part of the video, I will show you how to use solution of triangles.
But if you're happy with this method, that's all. If you want to know the solution of triangle, keep watching. If you're here, you're interested in the solutions of triangle method.
So how does that look like? Let me story you the equation. If you have a triangle like this, I'm going to talk about the cosine rule. And this line is A, this line is B, this line is C. Let's say this angle is capital...
b okay so cosine rule states that b square is equal to a square plus c square minus 2ac. Okay, so basically we're doing hopscotch or jumping across the triangle. I want to find this length b. So this length squared is these two sides a square plus c square minus two times a times c cos b.
Move it here, leave it space. Oops. Cos d. I'm going to apply it there, okay? So, I will say using, because I already drew the diagram.
Don't waste my solution of triangles or the cosine rule, okay? R squared. is equal to 28 square plus 95 square minus 2 times 28 times 95, whatever you write here, the other two sides, cos, what's the angle? This is the angle, the angle opposite to the side that you're looking for. So this is 125. Is it 125?
Is it 115? 115, my bad. Okay, because it's 180. minus 65 so 115 is cost 115 okay so you can press a caseo the calculator okay and uh if you press it properly press it with you now my slightly not so true calculator hang on let me move this a bit okay so cost 115 Okay now, so if I press my calculator, minus 2 times 2, 8 times 9, 5. Please make sure your calculator here is in degree, not radian. The rest, you just let calculator do the job. Square root answer.
Ta-da! 109.8. I got 11. 1, 1, 0. Okay. So I'm going to write this to 2SF or 3SF.
1, 0, 1, 1, 0. per second. So my drawing pretty good, quite accurate, I'm happy. Okay so you can always also use this to double check if you are strong in maths.
If you're not good in maths, it's okay guys, it's fine. Drawing a diagram is perfectly legit, just put your arrow there and measure. Bring your arrow, put your ruler, put your ruler there and measure.
I'm not going to edit that part out and then bring your projector. Alright so scale drawing method, use solution of a triangle to double check your answer. I will see you in the next video for the second method if you really don't like to draw.
Bye!