SOLUTION: The pilot of an airplane flies at a constant speed of 200 km/h at a bearing of S 40° E. There is a 42 km/h crosswind blowing E 20° N. What are the plane’s actual speed and directio

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Question 290412: The pilot of an airplane flies at a constant speed of 200 km/h at a bearing of S 40° E. There is a 42 km/h crosswind blowing E 20° N. What are the plane’s actual speed and direction? Please show all appropriate steps and diagrams. Watch out for the quadrant you are in so you have the right signs.
Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
The pilot of an airplane flies at a constant speed of 200 km/h at a bearing of S 40° E.
There is a 42 km/h crosswind blowing E 20° N.
What are the plane’s actual speed and direction? Please show all appropriate steps and diagrams.
------------------------
Plane DATA:
x vector = 200*cos(270+40) = 128.56
y vector = 200*sin(270+40) = -153.21
------------------------------------
Wind DATA:
x vector = 42*cos(20) = 39.47
y vector = 42*sin(20) = 14.37
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Conbining corresonding vectors:
x vector 128.56+39.47 = 168.03
y vector -153.21+14.37 = -138.84
------
distance = sqrt(168.03^2 + 138.84^2) = 217.97 km
angle = arctan(-138.84/168.03) = -39.57 degrees
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Cheers,
Stan H.