What Could Be the Mistake in Calculating Displacement Direction?

[rleung3]

Hi,

I solved this problem, but I don't agree with the book answer and can't seem to figure out what I did wrong.

An explorer in the dense jungles of equatorial Africa leaves his hut. He takes 40.0 steps at an angle 45.0 north of east (vector A), then 80.0 steps at an angle 60.0 north of west (vector B), then 53.0 steps due south (vector C). Calculate the direction of displacement.

I disagree with the answer in this problem. The answer is 15 degrees east of south, but I have solved it several times and I keep on getting 15 degrees west of north. I don't see how you would end in the the 4th quadrant. I keep ending up in the 2nd. Is this perhaps a mistake on the part of the book?

Here is what I did:

Ax = 40cos45 = 28.28
Ay=40sin45 = 28.28
Bx=80cos120 = -40
By = 80sin120 = 69.28
Cx = 0
Cy = -53

x-component = 28.28 - 40 = -11.72
y-component = 28.28 + 69.28 - 53 = 44.56

arctan(44.56/11.72) = 75.3 degrees north of west, or 15 degree west of south.

I was just sitting for a long time trying to find out where I went wrong but couldn't. Thanks so much.

Ryan

 

[andrevdh]

I agree with your findings.

 

[kyle8921]

,

Thank you for sharing your calculations and thought process. It seems like you have approached the problem correctly and your answer of 15 degrees west of north does make sense based on the given information. It is possible that there is a mistake in the book's answer or in the way they have presented the problem. As scientists, it is important for us to question and critically analyze information, so it is good that you have noticed this discrepancy and are trying to understand it. I would suggest double checking your calculations and considering the possibility of a mistake in the book. If you are still unsure, you can always consult with your instructor or a peer to get a second opinion. Keep up the good work!