Eli finds a map for a buried treasure. It tells him to begin at the old oak and walk 21 paces due west, 41 paces at an angle 45° S of W, 69 paces due north, 20 paces due east and 50 paces at an angle of 53° S of E, Determine the position of the buried treasure.

How would I solve this problem?

Just draw it out on paper?

The position of the BURIED treasure is underground. duh!

draw it out, then state that it is X paces this way

Draw the vectors out, starting from the tree, head to tail. Then draw a vector from the tree to the head of the last vector. This is the sum of all the other vectors. Use whatever method of adding vectors you want to find this "resultant".

This seems far more like math than physics.

Use a protractor for the angles.

Use trig sines and cosines to split each vector into its x and y (or north/south and east/west) components. Then all all the x' and y's up to get the two sides adjacent and opposite the hypotenuse that is the direct path to the final position. Use trig again to figure out the length of the triangles hypotenuse, and its angle from the x-axis. (or east)

If you're still having trouble when I get back from class, I'll give you a more detailed explanation of how to do it.

Unless I'm mistaken, the answer is 50 paces 37º North of West. Just to check. See what you get (if you even know how)

We just started on thermo, but we're only touching on non-mechanical portions. Going to focus on the mechanical portion of the AP exam.

So far, the biggest ***** is projectile motion. ****-all that's confusing.

Yeah, basically you are just making a bunch of triangles and using their hypotenuses. Until you get to 3d motion, nearly everything in physics is just triangles

I got that the treasure was buried pretty much at the same place you started. (0.1, 0.08) actually, but I didnt round as much as I think they wanted you to.

Here's what I did. First, I made a rough sketch of the paths. As you can see, the answer should be somewhere in the vicinity of the origin, even though my sketch is no where near being in scale.



Next, 3 of the vectors have only x or y components, so we will start with them. We'll make a simple graph so we can keep track of how many paces we take in the X direction, and how many in the Y direction. Note that when we go east or north, we are moving in the positive X or Y directions, respectively, and when we go west or south, we are moving in the negative X or Y directions, repsectively.



Now we need to figure out the X and Y components of the two vectors that are at angles. We do this using trig. Here is our triangle:



Remember that the Sine of an angle in a right triangle is equal to the ratio of the Opposite side over the Hypoteneuse, and the Cosine is the ratio of the Adjacent side over the Hypoteneuse. We know the angle and the length of the hypoteneuse, so we can easily set up an equation with one unknown and solve it.



In our case, the opposite angle is the Y component of our vector, so O = Y. (Make sure your calculator is in degrees mode and not radians, or else this equation will not work correctly!) Using a similar method, we can get an equation for the adjacent side A, which is also the X component.



Solving these equations for X and Y, yields us with results of 28.99 and 28.99, which makes sense, because Sin(45) = Cos(45). Now comes the tricky part... Because we were moving in the negative X direction, our 28.99 is actually -28.99. Also, because we were moving in the negative Y direction, that 28.99 also becomes -28.99. lets add these two values to our list.



Using the same method for the second vector at an angle, we find its X and Y components to be 30.99 and -39.93. I'll let you verify this on your own, because I dont feel like doing the entire problem for you. Lets add these final numbers to our list, and calculate the final position of the buried treasure by summing all of the X and Y components:



If you round -28.99 to -29, 30.09 to 30, -28.99 to -29, and -39.93 to -40, you will get (0,0) which I suspect is the answer your teacher is looking for.

Thanks DSettahr, the picture helped immensely. I guess the main problem I was having was that my picture wasn't exactly scaled as opposed to yours.

Here's mine...whee. I got a different answer :\



By the way, this is NOT TO SCALE

You can do it much easier if you convert it to cartesian with your calculator, then add the vectors that way...

Well, my answer's wrong, but so is DS' I think. I'll have to work it out a couple times to get it.

Yoshi's is definately wrong. He's got 29 + 30 = 69 on the left side of his image, when everyone knows that 29 + 30 really equals 59. In addition, he never bothered to figure out the X component of the final vector. His graph would appear to assume that its zero.

Way to kill my hopes and dreams DS.

Damn you DS. Damn you to hell. Stop being right.

From AIM:

[10:21::21:43:30] djyoshmo: I'm just not going to worry about it :p
[10:21::21:43:34] djyoshmo: leave it as is
[10:21::21:43:57] DSettahr: I'll take that as you accepting that my answer is correct. ;-)
[10:21::21:44:08] djyoshmo: no
[10:21::21:44:18] djyoshmo: I'm accepting you dashed my hopes and dreams
[10:21::21:44:27] djyoshmo: but if you're going to hound me, it's on!
[10:21::21:44:34] djyoshmo: *breaks out the pencil and paper
[10:21::21:44:35] djyoshmo: *

A few minutes later...

[10:21::21:50:13] djyoshmo: I hope you die in a fire
[10:21::21:50:16] djyoshmo:
[10:21::21:50:37] DSettahr: haha
[10:21::21:50:40] DSettahr: did you get the same answer as me?
[10:21::21:50:43] djyoshmo: shut up

I hate my life.

I came up with the same answer in 5 seconds with a piece of paper with stickmen pirates.

Well I did it all in Paint. So that took me a while.

<3 DS * 42

my way would be to :

plan a: once i know the general area, I would sweep the area with a metal detector.

If this doesn't work:

plan b: Find someone who knows and torture the info out of them.

Add vectors tip to tail. Once you see the orgin and the end, you draw a vector FROM the origin POINTING to the end and that is your final vector. If you think about it, you took the long way around. Finding the angle and the magnitued of the vector just uses some trig.

Components of vectors:
We have a vector a.

The x component is a*cos(theta), the y component is a*sin(theta) where a is the magnitude (size) of the vector.

Edit: Would Help if I read the question right.

The answer is .13 paces, 37.7512° N of E.
I think they were probably going for right where you sarted.

Drawn in AutoCAD. Scale accurate to four or five decimal places.

Too bad you were only about a day late with your answer. :p

Supposing the treasure was too deep to be tracked by your fancypants metal detectors...

What in the world could that be!?!

Me whacks DSettahr with Darth Slaw's shovel and quietly exits thread...

I never realized I would get this many replies from a physic problem. Massassians sure love their math....
Anyway DSettahr was right, the position was back at the original position (the oak tree).