 Hello everyone, this is Mr. Langdale here and you know the golf season may be over But that doesn't mean that we still can't talk about golf and physics So I thought I'd throw a problem here at you that deals with adding non-right angled vectors And I thought I'd make it about golf. So it's kind of the best of both worlds. You got your golf You got your physics. What more can you ask for? So in the first hole at the links in spruce Grove my home course LD hit his drive 314 yards not bad at 115 degrees Don't worry about the fact you've got a non-metric unit here This is going to work exactly the same if you're doing a question with meters or kilometers or centimeters or yards It doesn't matter. He did second shot 103 yards at 21 degrees east of north and of course he hold out for eagle. That's pretty common for me What was the golf balls resultant? Displacement okay, let's throw the word the in there. So when we're starting off with questions like this We want to begin by drawing diagrams. I'm going to make a diagram for 314 yards 115 degrees and then separate one for 21 degrees east of north. So let's deal with the first one here first 314 degrees or 314 yards 115 degrees. What does that look like? Well, let's do 115 degrees. It's got the square brackets around it here Which means it's going to be the rectangular coordinate system the RCS system That's always measured here from the positive x-axis first So I'm going through 90 degrees and then to get to 115 is going to be somewhere about there roughly, right? That's about 115. It's a little past 90. So that's roughly what my vector is going to look like. Yeah, that's 115 degrees Now doing trig with that isn't much good because I can't do simple right angle trigonometry with 115 degrees I have to use an acute angle on this less than 90 So I think I want this angle that's in here is the one I actually want Right, that's the angle that I would like to deal with so to figure that out I'm going to go through 90 and then what much how much more do I need to make 115? I would need 25 degrees more which means this angle in here is got to be 25 Now when I add 25 and 90 I get the 115 Okay, so I've got that vector drawn out now. Let's do the x and y components so I think this is going to be a good-looking x component there that'll work nicely and Maybe I'll use this y component there there. So that's my x. I got my y and I think I'll do some labeling here So this is going to be 314 yards Okay, there we go looks good Not bad now. Let's deal with the next one here Okay, 21 degrees east of north. So I'm going to start off at the east Sorry, I'm going to start off north. I'm going to go to the east by 21 degrees So starting north going to the east. That's what that's going to look like by 21 degrees And now again, I can put in my components. So there's my y component. There's my x component I've got two triangles drawn out I've got my x and y components and I can go ahead and quickly label this as 103 yards Now what I want to do next is I want to actually figure out what the x and components are So to do that, I'm going to use a little bit of sine a little bit of cosine I've already got the calculations done So I'm just going to erase them so you can see what I did here So for the top triangle here, there is my sine calculation That's going to allow me to find the x component I'd use sine here because I had x which was the opposite side to the angle that I was given So when I get my sine calculation, I do that, I get a negative 132.7021 yards Why is it negative? This is the most important part of the question It's the part that kids usually forget It's negative because this vector is going to the left So you've got to remember, any time your vectors are going left or down, make them negative Forgetting to do that is probably the biggest mistake students make on these problems What about the y component? Well, that side is adjacent to the angle So I'm going to use cosine, cosine is adjacent over hypotenuse Hypotenuse is 314 yards, multiply those out 284.5806 yards Notice I'm keeping four guard digits or four numbers after the decimal So that my final answer comes out to be correct Now what about for this other triangle down here? Same idea, cosine, sine, sine is used for the x because x is the opposite side Cosine is used for the y because it's the adjacent side And they're both positive, so I left them as both positives in the question Sorry, my numbers here So I've got my triangles drawn out separately I've broken the vectors into x and y components And I've actually figured out what they are here Making sure that if it's going left or down, it's negative And right or up is positive Now I'm going to take my next step here Is just going to be taking those two x's and adding them together So here's my x total The total of the two x's from my first triangle to my second triangle Worked out to 95.7902 yards And for my two y's, I added those together 380.7394 yards So there's an x total and a y total Now I can take those two totals and I can make a final triangle And this is what I'm going to find my answer from It's a nice right angle triangle And to find the resultant, just like we did for regular old right angle problems I can use the Pythagorean formula So there we go, I set up the Pythagorean formula And I get the resultant to be 393 yards To find the angle theta, which is going to be down in the corner here Between the two tails, there's my theta I'm going to use the inverse tan function Because I'm using tan because I have the opposite and adjacent sides of the triangle here And I'm getting 75.9 degrees You can either call that north of west North of west works fine Moving to the north from the westerly direction Or 104 degrees rcs If you think about this, this would be going through 90 degrees And then an extra 4 degrees roughly if you were to round it To get up to 76, which is about 75.9 So those steps again You want to draw out your two vectors You want to break them into x and y components Make sure that if the x component or the y component is going left or down You make it a negative Then take your two x's and add them together And take your two y's and add them together And then you've just got a simple right angle triangle problem Where you can figure out the resultant using the Pythagorean formula And you can figure out the angle using tangent So I hope that helped If you're looking for more questions on adding non-right angle vectors Check out my website at LDindustries.ca