# Challenging Vector Problem

1. Jan 30, 2008

### Cathartics

******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?

(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...

2. Jan 30, 2008

### robphy

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. Jan 30, 2008

### Cathartics

It's still unclear to me, despite my several attempts i am unable to solve it. Please help help help!!!!

4. Jan 30, 2008

### lisab

Staff Emeritus
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. Jan 30, 2008

### robphy

I think vector B is correct but Vector C is wrong.