Kim S.
asked • 04/25/15Problem solving
Boat:initially traveling 150 mph 100degrees north east, suddenly enters a region where the wind is blowing 50 mikes south west. What is the resultant direction of the boat. I considered using the law of cosine formula, but I am confused how I would calculate the resultant direction if I went in that direction. Would the law of cosine be the wrong way to go? If not not, how should I find the resultant direction from LoC, considering the resultant direction is found by using the tangent after finding the magnitude? I'm just unsure how I should go about this?
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1 Expert Answer
Raymond B. answered • 11/17/22
Tutor
5
(2)
Math, microeconomics or criminal justice
if this isn't your problem it's very similar
N10E at 150 means 80 degree angle with x axis
P=<150cos80, 150sin80>= plane's vector
S45W at 50
W=<-50cos45, -50sin45>= wind's vector
resultant vector = P+W
= <150cos80-50cos45, 150sin80-50sin45>
=<150cos80-25sqr2, 150sin80-25sqr2>
=<x,y>
direction = angle with the x axis = tan^-1(y/x)
direction =N(90-tan^-1(y/x)E
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Derek S.
Also, is the wind blowing 50 mph southwest at any certain angle, or just 45 degrees between south and west? In either case, are we assuming the wind and the water are both moving identically?
You do seem to be on the right track with the law of cosines though, as that should give you the answer rather easily after you construct a triangle diagram.
04/25/15