Vector Components Homework: Find Displacement for Bob to Return to Start Point

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Homework Help Overview

The problem involves calculating the displacement required for Bob to return to his starting point after walking in multiple directions: 200m south, 400m southwest, and 200m at an angle of 30 degrees east of north. The subject area pertains to vector components and trigonometry.

Discussion Character

  • Exploratory, Assumption checking, Mathematical reasoning

Approaches and Questions Raised

  • Participants discuss the components of Bob's movements, particularly focusing on how to derive the components for the 400m southwest leg of the journey. There is an exploration of angles and the implications of assuming certain angles for calculations.

Discussion Status

The discussion is ongoing, with participants seeking clarification on the derivation of vector components, particularly for the southwest movement. Some guidance has been offered regarding visualizing the problem through sketches or scale drawings, but no consensus has been reached on the specific calculations.

Contextual Notes

There is a mention of a solutions manual that provides specific component values, which raises questions about the assumptions made regarding angles in the problem. Participants are navigating through these assumptions and the implications for their calculations.

ch2kb0x
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Homework Statement



Bob walks 200m south, walks 400m southwest, walks 200m in a direction 30 degrees east of north.
Use either trig or components to find displacement that will return bob to his starting point by the most direct route.

Homework Equations





The Attempt at a Solution


For this problem, I was able to find components for C, which is (200sin30)i + (200cos30)j,
but how do I find components for B. could somebody show me the steps to getting B components. I can do the rest.
 
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B components?
Just picture this its very simple
200 south
...|
...|
.../ 400 southwest (assuming 45deg)
../
./
/then 30deg east of north, which i can't draw.

After explaining this I'm inclined to think that your question is what the angle measure is of 400m southwest, because they ask something else in the latter part of the question I'm inclined to think that they just want you to assume 45deg.
 
Sorry i didnt let you know what B was. B is the 400m southwest. In the solutions manual, they obtained (100) i + (173) j for the 200m in 30 degrees east of north which is equivalent to (200sin30)i + (200cos30)j. But they also had -(283)i - (283)j for 400m southwest. My question, is how is "-(283)i - (283)j" derived. It would be nice if someone could walk me through.
 
ch2kb0x said:
Sorry i didnt let you know what B was. B is the 400m southwest. In the solutions manual, they obtained (100) i + (173) j for the 200m in 30 degrees east of north which is equivalent to (200sin30)i + (200cos30)j. But they also had -(283)i - (283)j for 400m southwest. My question, is how is "-(283)i - (283)j" derived. It would be nice if someone could walk me through.

Did you draw a picture of B with all the distances and angles marked?

(If a sketch doesn't help, try a scale drawing, and you'll see what's going on.)
 

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