Challenging Vector Problem

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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.
 

Answers and Replies

  • #2
robphy
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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.
 
  • #3
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It's still unclear to me, despite my several attempts i am unable to solve it. Please help help help!!!!
 
  • #4
lisab
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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."
 
  • #5
robphy
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I think vector B is correct but Vector C is wrong.
 

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