Mountain climbing Vector problem

[bluewolf]

Hey
I'm new to this forum and I have a question on my homework if anyone could help that would be very cool:) Ok here is the problem

A mountain climbing expedition establishes a base camp and two intermediate camps, A and B. Camp A is 11,200m east of and 3200m above base camp. Camp B is 8400m east of and 1700m higher than Camp A. Determine the displacement between base Camp B.

We are supposed to solve and sketch a diagram for it. What I did was did a I made a point for base camp and a point for camp A and then did a resultant vector thing. Then I took the point A and then made a triangle with point B (resultant vector thingy again) and then did pathagarian theorum on them and then added the two together. I don't know if I did it right the #s came out really big...

 

[e(ho0n3]

Show us your calculation.

 

[berkeman]

It sounds like you are doing them correctly, so just check your math again to see if you can spot the error. Remember to take the square root at the end of applying the Pythagor... Pythagorean... (sp?) theorem.

BTW, the best way to make a sketch of this kind of vector addition is to learn to sketch the x,y,z axes in a kind of a 3-D perspective. It helps to do it on engineering or gridded paper. Draw the vertical z axis straight up, the horizontal x-axis straight out to the right, and the y-axis kind of up and right at a 45degree or so angle. Then you can mark off tick marks for distances directly on the x and z axes, and mark them off in perspective on the y axis. Then mark each of your 3-D points, and that helps you visualize the associated position vectors in 3-D.

 

[e(ho0n3]

If think a 3D graph is not necessary for this problem since both camps are in the same general direction (east).

 

[berkeman]

If think a 3D graph is not necessary for this problem since both camps are in the same general direction (east).

Good point. I didn't read the original question closely enough to notice that both vectors are in the same E-W plane. Still, I wanted to be sure that he had that tool available for his ongoing (I guess future?) work with vectors in 3-D space.

 

[bluewolf]

okay well this is what I did

(8400)^2 + (1700)^2
then I took the square root of that
(11200)^2+ (3200)^2
then I took the square root of that and then added the two together.

Also I was wondering what does it mean when it says displacement? Because I have another problem that says displacement in it too.

 

[berkeman]

Displacement means the movement from one place to another. In your original post (OP), I think they are asking for the displacement from camp A to B, but there is a typo in your problem statement that makes this hard to know for sure. I think the way the problem is stated makes it easier for you to solve for the displacement, since they tell you how far camp B is from A in both the horizontal and vertical directions. They could have made it a little harder by giving you camp B's position with respect to base camp, but whatever.

So the displacement you are solving for is the hypotenuse of the triangle formed by A and B (and the point directly to the east of A and below B.

 

[bluewolf]

ok, thanks. That makes sense but in this other problem that I have it goes a bunch of different directions so what do you do then? Do you calculate from the starting point to the finishing point or what because it kind of makes a boxish shape (it goes east, south, west, then north)

 

[berkeman]

In the general case, you need to use vector addition and subtraction, and that is easist for you now in a rectangular coordinate system. So a vector in the x-y-z coordinate system I described earlier is expressed as (x,y,z) if the vector starts at the origin (0,0,0) and ends at (x,y,z). If the vector starts at point A and ends at point B, then that vector is written something like (xB-xA,yB-yA,zB-zA). Note that you can also get that vector by subtracting the vector from the origin out to A (xA,yA,zA) from the vector from the origin out to B (xB,yB,zB).

So in general, you write the position vectors to all the points, and then do the subtractions to get the final displacement vectors. The length of the vector is found using the Pythagorus theorum.

If you are working mostly in hiking type problems like your OP, then you would use East-North-Altitude coordinates.

 

[bluewolf]

Gotcha:) I think that I was just making it harder than it really was.