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.