How Do You Calculate the Fourth Displacement in Vector Addition?

[Fireworkslvr]

Homework Statement

" A spelunker is surveying a cave. he follows a passage that goes 210 meters straight west, then 180 meters in a direction 45 degrees east of west, then 110 meters at 60 degrees east of south. After a fourth unmeasured displacement he finds himself back where he started. Use the method of components to determine the fourth displacement (magnitude and direction). "

Homework Equations

The Attempt at a Solution

I have looked around for information on solving this, but am unsure about how to go about finding the other angles to find the magnitude or direction, and am not sure about finding the last dimension. I know I am supposed to show you that i have tried this and believe me I have, but I am new to physics and am pretty much confused on where to even begin this problem.

Thanks for all help.

 

[rootX]

Homework Statement

" A spelunker is surveying a cave. he follows a passage that goes 210 meters straight west, then 180 meters in a direction 45 degrees east of west, then 110 meters at 60 degrees east of south. After a fourth unmeasured displacement he finds himself back where he started. Use the method of components to determine the fourth displacement (magnitude and direction). "

Homework Equations

The Attempt at a Solution

I have looked around for information on solving this, but am unsure about how to go about finding the other angles to find the magnitude or direction, and am not sure about finding the last dimension. I know I am supposed to show you that i have tried this and believe me I have, but I am new to physics and am pretty much confused on where to even begin this problem.

Thanks for all help.

break each vector into x-y components
{
x-comp = vector magnitude x cos theta
y-comp = v mag x sin theta
},
and then from the question you know that:
x1+x2+x3+x4=0
y1+y2+y3+y4=0

so solve for x4 and y4

 

[Fireworkslvr]

break each vector into x-y components
{
x-comp = vector magnitude x cos theta
y-comp = v mag x sin theta
},
and then from the question you know that:
x1+x2+x3+x4=0
y1+y2+y3+y4=0

so solve for x4 and y4

Thanks, that helps a lot!

 

[quozzy]

Another nice way to do it (if you've got the time) is to solve it graphically, by drawing a scaled version of the problem out. Even if you end up solving it numerically, a sketch often helps by showing you roughly what you should be getting.