Two beetles run across flat sand, starting at the same point

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Homework Help Overview

The problem involves two beetles running across flat sand, with specific distances and angles for their movements. The objective is to determine the necessary second run of beetle 2 to match the final position of beetle 1.

Discussion Character

  • Exploratory, Problem interpretation, Assumption checking

Approaches and Questions Raised

  • Participants discuss setting up vector equations to relate the displacements of both beetles. There is an exploration of using triangles to find the necessary components of the vectors involved.

Discussion Status

The discussion is ongoing, with participants attempting to clarify the relationships between the vectors and exploring different methods to approach the problem. Some have raised questions about the total distances traveled by each beetle in both the east and north directions.

Contextual Notes

There is mention of a diagram included in the original post, which may provide additional context for the vector relationships being discussed. The problem may involve assumptions about the coordinate system being used.

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Homework Statement


Two beetles run across flat sand, starting at the same point. Beetle 1 runs 0.50 m due east, then 0.80 m at 30◦ north of due east. Beetle 2 also makes two runs; the first is 1.6 m at 40◦ east of due north. What must be (a) the magnitude and (b) the direction of its second run if it is to end up at the new location of beetle 1?

Homework Equations

The Attempt at a Solution


I set up the vector, but the problem i am having is where to start for finding the answer i need. On the picture which is included below.
 

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Let A and B be the two displacements of beetle 1. Let C and D be the two displacements of beetle 2.

Can you write a single vector equation that shows how these 4 vectors are related?
 
TSny said:
Let A and B be the two displacements of beetle 1. Let C and D be the two displacements of beetle 2.

Can you write a single vector equation that shows how these 4 vectors are related?

I could but i am trying to use triangles to find the answers.
 
How far east did beetle 1 go in total?
How far north did beetle 1 go in total?

How far east did beetle 2 go in its first run?
How far north did beetle 2 go in its first run?
 

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