Challenging Vector Problem: How Can Beetle 2 Reach the New Location of Beetle 1?

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Homework Help Overview

The problem involves two beetles moving on a flat surface, with specific distances and angles described for their movements. The goal is to determine the necessary magnitude and direction of Beetle 2's second run to reach the same location as Beetle 1, based on vector calculations.

Discussion Character

  • Exploratory, Assumption checking, Mathematical reasoning

Approaches and Questions Raised

  • Participants discuss the vector components of the beetles' movements, with attempts to calculate resultant vectors and angles. There are questions about the correct interpretation of angles relative to cardinal directions and the setup of the vector equations.

Discussion Status

Some participants have provided insights into the differences between angles measured from "north" versus "east," suggesting a need for clarification in the calculations. There is ongoing exploration of the vector components, with no consensus reached on the correct approach yet.

Contextual Notes

Participants express confusion regarding the angles and their respective orientations, indicating potential misunderstandings in the problem setup. There is a request for detailed guidance, but no specific solutions have been provided.

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******Challenging Vector Problem******

Two beetles run across flat sand, starting at the same point. Beetle 1 runs 0.50 m due east, then 0.82 m at 26° north of due east. Beetle 2 also makes two runs and the first is 1.6 m at 43° east of due north.
(a) What must be the magnitude of its second run if it is to end up at the new location of beetle 1?
Answer in m

(b) In what direction must it run?
Answer in ° (counterclockwise from due east)

I have made numerous attempts to the problem here is one of my attempts

Vector A =.50 i + 0 j
Vector B = .82 cos26 i + .82 sin26 j = .7370 i + .3594 j
Vector C = 1.6 cos43 i + 1.6 sin43 j = 1.1701 i + 1.0911 j

I did A+B - C and that was R = .0669 i + (-.7317) j
|R| = .7347m and angle = 84.77

What am i doing wrong when i plug the answers online it says I'm wrong! Please please help me on this. Can you please provide the exact answer along with the meathod i want to see the whole thing done...
Thanks in advance.
 
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Note that "north of due east" is different from "east of due north".
Draw in the angle in both cases... then look at your components.
 
It's still unclear to me, despite my several attempts i am unable to solve it. Please help help help!
 
The angle given for beetle 2 is measured off of "north." Your calculations are set up as if the angle is measured off of "east."

Use the angle that beetle 2 makes with "east" instead of "north."
 
I think vector B is correct but Vector C is wrong.
 

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