How Do You Calculate the Return Path in Vector Addition?

[Resmo112]

A scout troop is practicing its orienteering skills with map and compass. First they walk due east for 1.3 km. Next, they walk 42° west of north for 3.7 km. How far and in what direction must they walk to go directly back to their starting point?
Distance km
Direction ° east of south

Homework Equations

well I figure my scout troop made a right triangle and I need to put it into a^2+b^2=c^2 I've got 1.3^2 + b^2= 3.7^2 after all the math I get 12 and square root that and you've got 3.46 but apparently that's wrong and I don't know how else to solve it. I really don't get these at all so if anyone can help me add vectors (feel like an idiot I'm 30 and can't add) I'd appreciate it.

 

[Chopin]

Well, you can start by drawing it on a piece of graph paper. Try to be somewhat accurate as to the lengths of the lines, and the angles involved. Once you have a picture that you can look at, it will become clearer what sort of equation you'll need to do, and then you can solve it exactly (hint: it's not a right triangle).

 

[Resmo112]

but if I'm headed east, and I'm then heading north of west and I have to set up my vectors tip to tail how isn't it a right triangle? I don't get this, I'm hoping for a little more help.

 

[Resmo112]

the interweb gave me this help




For a triangle with length of sides a, b, c and angles of α, β, γ respectively, given two known lengths of a triangle a and b, and the angle between the two known sides γ (or the angle opposite to the unknown side c), to calculate the third side c, the following formula can be used:




If the lengths of all three sides of any triangle are known the three angles can be calculated:


apparently it cut out the images. but it has an "arccos" which I don't even know what that is?

 

[Karlx]

Hi Resmo112.
Better you follow Chopin's advice.
If you draw accurately the scout's way, it will help you to solve the problem.

 

[Chopin]

The formula you mentioned is called the Law of Cosines. It could help you with part of your problem here, but not all of it. Also, if the intent of this problem is to give you insight into using vectors, you will learn more if you do not use that formula, and go back to thinking of each leg of the path as a separate vector.

You're right that you have to put them tip to tail, but in general that isn't going to be a right triangle. Imagine walking 500 feet in one direction, then turning 170 degrees around (so you're only 10 degrees off from having turned completely around.) Then you walk 10 feet and stop, and finally walk from that point back to the start. You'll have walked in a triangle, but it's certainly not going to be a right triangle, it's going to be some weird little flat one. The same sort of thing is happening here (although the triangle won't be shaped exactly like that.)

Just to clarify, when they say "42 degrees west of north", they mean "off on some diagonal direction that's sort of northwest-ish". Were you interpreting it that way, or were you trying to draw a line straight north?

 

[Resmo112]

I didn't need to follow Chopin's advice I'd already tried to draw it out, I'm not getting the right drawing even because I keep getting right triangles.

ok As far as "north of west" I drew a line with an angle about 42 degrees from the tip of my east line in a northwestardly direction. so definitely not straight north. I guess the problem is to give me a good idea of solving vectors but the problem is after I draw it out, I have no Idea what to do if I can't use the pythagorean theorem. I've been through all the notes for the class and they're no help because he just jumps into using cos sin and tan but never explaining how or why we use them, and I've been to three different teachers who can't really seem to help me either. I swear I'm not this stupid, I just can't figure out where to even start on a lot of these

 

[Chopin]

Ok, well then step 1 is making sure you have the correct drawing. If you don't have the right picture in your head, then you'll definitely have problems getting the right answer.

Can you draw your diagram in Paint or something like that, and then post it here? I don't know if PF has a way to upload images or not, but if not you can just use some site like Imageshack. The diagram doesn't have to be perfect, it can just be some crappy picture with a few lines on it. But it sounds to me like you have a different picture in your mind of what this looks like than I do, so comparing notes will be the first step in finding a solution.

[Edit: Looks like you can attach files to posts, so you shouldn't have to use Imageshack after all.]

 

[Resmo112]

I can scan something let me see what I can do

 

[Resmo112]

[PLAIN]http://img534.imageshack.us/img534/4254/photoon20110127at1636.jpg

 

[Chopin]

That seems to have gotten flipped around during scanning, but I get the idea. You have drawn it such that the scouts end up directly north of where they started. Are you sure that is correct? Try making another version of your diagram, but actually use a ruler to make the lines--pretend a kilometer is an inch, and make a diagram where they go over by 1.3 inches, and then up on a diagonal by 3.7 inches. You can be a little bit off on the lengths to make it easier on yourself (1.25 inches and 3.75 inches will be close enough)--the important thing is to figure out whether they're going to end up being directly north of where they started, or whether they'll be to the east or to the west of it.

 

[Resmo112]

I'll have to go get a ruler then I don't seem to have any measuring devices around here. Measurements or not even if I got the measurements right I still don't know where to go from there, been working on a 16 problem HW assignment since 1 i got 3 done

 

[Chopin]

Eh, it doesn't have to be a ruler...just make a few basically equally-spaced marks on a piece of paper and use that. This is just a rough guide to make sure you know what's going on, so it doesn't have to be super-accurate.