"While surveying a cave, a spelunker follows a passage 190 m straight west, then 210 m in a direction 45.0 degrees east of south, and then 270 m at 30.0degrees east of north. After a fourth unmeasured displacement, she finds herself back where she started. Use vector components to find the magnitude and direction of the fourth displacement."

I've tried this a few times and keep getting it wrong. I realize the resulting Rx and Ry should both be negative, but mine are not. Any help? Thanks!

Question

"While surveying a cave, a spelunker follows a passage 190 m straight west, then 210 m in a direction 45.0 degrees east of south, and then 270 m at 30.0degrees east of north. After a fourth unmeasured displacement, she finds herself back where she started. Use vector components to find the magnitude and direction of the fourth displacement."

I've tried this a few times and keep getting it wrong. I realize the resulting Rx and Ry should both be negative, but mine are not. Any help? Thanks!

anonymous · Answer

use a 2D design and drafting software , this question is like a puzzle :)

anonymous · Answer

Quite easy, frankly! Draw a picture with the vectors represented. I am working on it for fun!

anonymous · Answer

I tried drawing it on paper, unfortunately I feel like I am making a mistake on one of my angles I am putting into Cos and Sin.

anonymous · Answer

SunMan provided me with an answer in Group Chat and was very helpful!

anonymous · Answer

$$\sin^{-1} (85.33/126.6) = 42.4$$
     (we spoke about the 126.6 and 85.33, you know them)

but here we should 90-42.4=47.6 :)