How Do You Calculate the Magnitude of Vector B in a Closed Hiking Trail Problem?

[malik123]

Homework Statement

The route followed by a hiker consists of three displacement vectors A, B and C. Vector A is along a measured trail and is 2500 m in a direction 25.8° north of east. Vector B is not along a measured trail, but the hiker uses a compass and knows that the direction is 43.1° east of south. Similarly, the direction of vector C is 32.2° north of west. The hiker ends up back where she started, so the resultant displacement is zero, or A + B + C = 0. Calculate the magnitude of vector B.

Homework Equations

This is for my physics course. The teacher expects us to know vectors already, and I have never had them. I have tried for over 3 hours to solve this question. No luck.

The Attempt at a Solution

I realize that the vectors form a triangle since the displacement is 0. So I tried to assign the correct values to the interior of the triangle, and then use the law of sines to find the magnitude of vector b.

I bet there is a better way to solve this but I have no idea.

Please help me guys!

Thanks!

 

[Quincy]

I realize that the vectors form a triangle since the displacement is 0. So I tried to assign the correct values to the interior of the triangle, and then use the law of sines to find the magnitude of vector b.

That's the correct way to do it.

 

[malik123]

That's the correct way to do it.

I guess I am just getting the incorrect angles.

 

[hage567]

malik123, show your work so we can see what you've done. We can look for your error.

 

[malik123]

malik123, show your work so we can see what you've done.

Amazingly quick response. Ok! one sec

 

[malik123]

Ok the angles I got were:

58 degrees, opposite to the B side.
14.7 opposite to 2500.
107.3 opposite to the x axis.

I found these using alternate angles. I think I most certainly did it wrong, cause my answer is not correct.

Then I used the law of sines,

Sin 14.7/2500 = sin58/ B

B = 8354.9

Which is wrong!

Just so you don't get the wrong idea. I am not trying to come get a free answer. I just need a little help or direction, and then I can try once again to solve the problem!

Thanks

 

[DarylMBCP]

I found these using alternate angles. I think I most certainly did it wrong, cause my answer is not correct.

Show how u used Laws of Sine cos. I found the angles to be the same as yrs.

 

[malik123]

Show how u used Laws of Sine cos. I found the angles to be the same as yrs.

I just did. So what did I do wrong?

 

[DarylMBCP]

Lol, I was typing my comment while u were typing yr solution. K, anw, tht's the same answer I got.

 

[malik123]

Lol, I was typing my comment while u were typing yr solution. K, anw, tht's the same answer I got.

Thanks for the help.

For some reason though, the online answer checker won't accept this answer as correct. =(

 

[Kennyh]

Thanks for the help.

For some reason though, the online answer checker won't accept this answer as correct. =(

Hey do you go to UGA or use a website called loncapa?

 

[malik123]

Hey do you go to UGA or use a website called loncapa?

Loncapa

 

[Jebus_Chris]

Your interior angles are wrong, 58 is right though. Draw a picture of where A and B meet. Draw a horizantal line at the vertex and label what you know.

 

[malik123]

Your interior angles are wrong, 58 is right though. Draw a picture of where A and B meet. Draw a horizantal line at the vertex and label what you know.

I tried again and I keep getting the same angles.

I don't know what I am doing wrong!